1. Review on Exponents

2. Review on Exponents
Let’s review the basics of exponential notation.

3. Review on Exponents
Let’s review the basics of exponential notation.
The quantity A multiplied to itself N times is written as AN.
A x A x A ….x A = AN exponent
N times base

4. Review on Exponents
Let’s review the basics of exponential notation.
The quantity A multiplied to itself N times is written as AN.
A x A x A ….x A = AN exponent
N times base
Rules of Exponents

5. Review on Exponents
Let’s review the basics of exponential notation.
The quantity A multiplied to itself N times is written as AN.
A x A x A ….x A = AN exponent
N times base
Rules of Exponents
Multiply–Add Rule:
Divide–Subtract Rule:
Power–Multiply Rule:

6. Review on Exponents
Let’s review the basics of exponential notation.
The quantity A multiplied to itself N times is written as AN.
A x A x A ….x A = AN exponent
N times base
Rules of Exponents
Multiply–Add Rule: ANAK = AN+K
Divide–Subtract Rule:
Power–Multiply Rule:

7. Review on Exponents
Let’s review the basics of exponential notation.
The quantity A multiplied to itself N times is written as AN.
A x A x A ….x A = AN exponent
N times base
Rules of Exponents
Multiply–Add Rule: ANAK = AN+K
AN = AN – K
Divide–Subtract Rule: AK
Power–Multiply Rule:

8. Review on Exponents
Let’s review the basics of exponential notation.
The quantity A multiplied to itself N times is written as AN.
A x A x A ….x A = AN exponent
N times base
Rules of Exponents
Multiply–Add Rule: ANAK = AN+K
AN = AN – K
Divide–Subtract Rule: AK
Power–Multiply Rule: (AN)K = ANK
x9

9. Review on Exponents
Let’s review the basics of exponential notation.
The quantity A multiplied to itself N times is written as AN.
A x A x A ….x A = AN exponent
N times base
Rules of Exponents
Multiply–Add Rule: ANAK = AN+K
AN = AN – K
Divide–Subtract Rule: AK
Power–Multiply Rule: (AN)K = ANK
9x5 =x14 , x9 = x9–5 = x4, and (x9)5 = x45.
For example, x x5

10. Review on Exponents
Let’s review the basics of exponential notation.
The quantity A multiplied to itself N times is written as AN.
A x A x A ….x A = AN exponent
N times base
Rules of Exponents
Multiply–Add Rule: ANAK =AN+K
AN = AN – K
Divide–Subtract Rule: AK
Power–Multiply Rule: (AN)K = ANK
9x5 =x14 , x9 = x9–5 = x4, and (x9)5 = x45.
For example, x x5
These particular operation–conversion rules appear often in
other forms in mathematics.

11. Review on Exponents
Let’s review the basics of exponential notation.
The quantity A multiplied to itself N times is written as AN.
A x A x A ….x A = AN exponent
N times base
Rules of Exponents
Multiply–Add Rule: ANAK =AN+K
AN = AN – K
Divide–Subtract Rule: AK
Power–Multiply Rule: (AN)K = ANK
9x5 =x14 , x9 = x9–5 = x4, and (x9)5 = x45.
For example, x x5
These particular operation–conversion rules appear often in
other forms in mathematics. Hence their names, the Multiply–
Add Rule, the Divide–Subtract Rule, the Power–Multiply Rule,
are important.

12. Review on Exponents
Let’s review the basics of exponential notation.
The quantity A multiplied to itself N times is written as AN.
A x A x A ….x A = AN exponent
N times base
Rules of Exponents
Multiply–Add Rule: ANAK =AN+K
AN = AN – K
Divide–Subtract Rule: AK
Power–Multiply Rule: (AN)K = ANK
9x5 =x14 , x9 = x9–5 = x4, and (x9)5 = x45.
For example, x x5
These particular operation–conversion rules appear often in
other forms in mathematics. Hence their names, the Multiply–
Add Rule, the Divide–Subtract Rule, the Power–Multiply Rule,
are important. Let’s extend the definition to negative and
fractional exponents.

13. The Exponential Functions
A1
Since A1 = 1

14. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0

15. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.

16. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1

17. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0
Since AK AK

18. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K,
Since AK AK

19. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A

20. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k
Since ( A )k = A = (A1/k )k,

21. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k k
Since ( A )k =A= (A1/k )k, hence A1/k = A.

22. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k k
Since ( A )k =A= (A1/k )k, hence A1/k = A.
k
Fractional Powers: A1/k = A.

23. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k k
Since ( A )k =A= (A1/k )k, hence A1/k = A.
k
Fractional Powers: A1/k = A.
For a general fractional exponent, we interpret the operations
step by step by doing the numerator of the exponent last.

24. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k k
Since ( A )k =A= (A1/k )k, hence A1/k = A.
k
Fractional Powers: A1/k = A.
For a general fractional exponent, we interpret the operations
step by step by of the exponent last.

25. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k k
Since ( A )k =A= (A1/k )k, hence A1/k = A.
k
Fractional Powers: A1/k = A.
For a general fractional exponent, we interpret the operations
step by step by doing the numerator of the exponent last.
Example A. Simplify.
a. 9–2 =
b. 91/2 =
c. 9 –3/2 =

26. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k k
Since ( A )k =A= (A1/k )k, hence A1/k = A.
k
Fractional Powers: A1/k = A.
For a general fractional exponent, we interpret the operations
step by step by doing the numerator of the exponent last.
Example A. Simplify.
a. 9–2 = 12 = 1
9 81
b. 91/2 =
c. 9 –3/2 =

27. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k k
Since ( A )k =A= (A1/k )k, hence A1/k = A.
k
Fractional Powers: A1/k = A.
For a general fractional exponent, we interpret the operations
step by step by doing the numerator of the exponent last.
Example A. Simplify.
a. 9–2 = 12 = 1
9 81
b. 91/2 = √9 = 3
c. 9 –3/2 =

28. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k k
Since ( A )k =A= (A1/k )k, hence A1/k = A.
k
Fractional Powers: A1/k = A.
For a general fractional exponent, we interpret the operations
step by step by doing the numerator of the exponent last.
Example A. Simplify.
a. 9–2 = 12 = 1
9 81
b. 91/2 = √9 = 3
c. 9 –3/2 =

29. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k k
Since ( A )k =A= (A1/k )k, hence A1/k = A.
k
Fractional Powers: A1/k = A.
For a general fractional exponent, we interpret the operations
step by step by doing the numerator of the exponent last.
Example A. Simplify.
a. 9–2 = 12 = 1
9 81 Pull the numerator outside to
take the root and simplify the
b. 91/2 = √9 = 3 base first.
c. 9 –3/2 = (9½)–3

30. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k k
Since ( A )k =A= (A1/k )k, hence A1/k = A.
k
Fractional Powers: A1/k = A.
For a general fractional exponent, we interpret the operations
step by step by doing the numerator of the exponent last.
Example A. Simplify.
a. 9–2 = 12 = 1
9 81 Pull the numerator outside to
take the root and simplify the
b. 91/2 = √9 = 3 base first.
c. 9 –3/2 = (9½)–3 = 3–3

31. The Exponential Functions
A1
Since A1 = 1 = A1 – 1 = A0, we obtain the 0-power Rule.
0-Power Rule: A0 = 1
1 = A0 = A0 – K = A–K, we get the Negative Power Rule.
Since AK AK
Negative Power Rule: A–K = 1 K A
k k
Since ( A )k =A= (A1/k )k, hence A1/k = A.
k
Fractional Powers: A1/k = A.
For a general fractional exponent, we interpret the operations
step by step by doing the numerator of the exponent last.
Example A. Simplify.
a. 9–2 = 12 = 1
9 81 Pull the numerator outside to
take the root and simplify the
b. 91/2 = √9 = 3 base first.
c. 9 –3/2 = (9½)–3 = 3–3 = 13 = 1
3 27

32. Fractional Exponents
The operation of taking power may be passed to factors.

33. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN

34. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN
For example, (2*3)2 = 22*32 = 36.

35. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN
For example, (2*3)2 = 22*32 = 36.
However the operation of taking power does not pass to terms.

36. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN
For example, (2*3)2 = 22*32 = 36.
However the operation of taking power does not pass to terms.
For example, (2 + 3)2 ≠ 22 + 32.

37. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN
For example, (2*3)2 = 22*32 = 36.
However the operation of taking power does not pass to terms.
For example, (2 + 3)2 ≠ 22 + 32.
In the example below, we use these rules to collect exponents.

38. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN
For example, (2*3)2 = 22*32 = 36.
However the operation of taking power does not pass to terms.
For example, (2 + 3)2 ≠ 22 + 32.
In the example below, we use these rules to collect exponents.
Example B. Simplify the exponents.
x(x1/3y3/2)2
x–1/2y2/3

39. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN
For example, (2*3)2 = 22*32 = 36.
However the operation of taking power does not pass to terms.
For example, (2 + 3)2 ≠ 22 + 32.
In the example below, we use these rules to collect exponents.
Example B. Simplify the exponents.
Do not covert the
x(x1/3y3/2)2 exponents into radicals.
We are to collect them
x–1/2y2/3 using arithmetic.

40. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN
For example, (2*3)2 = 22*32 = 36.
However the operation of taking power does not pass to terms.
For example, (2 + 3)2 ≠ 22 + 32.
In the example below, we use these rules to collect exponents.
Example B. Simplify the exponents.
2*1/3 2*3/2
x(x1/3y3/2)2 x*x2/3y3
–1/2y2/3
= –1/2 2/3
x x y

41. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN
For example, (2*3)2 = 22*32 = 36.
However the operation of taking power does not pass to terms.
For example, (2 + 3)2 ≠ 22 + 32.
In the example below, we use these rules to collect exponents.
Example B. Simplify the exponents.
2*1/3 2*3/2 1+2/3
x(x1/3y3/2)2 x*x2/3y3 x5/3y3
–1/2y2/3
= –1/2 2/3 = –1/2 2/3
x x y x y

42. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN
For example, (2*3)2 = 22*32 = 36.
However the operation of taking power does not pass to terms.
For example, (2 + 3)2 ≠ 22 + 32.
In the example below, we use these rules to collect exponents.
Example B. Simplify the exponents.
2*1/3 2*3/2 1+2/3
x(x1/3y3/2)2 x*x2/3y3 x5/3y3
–1/2y2/3
= –1/2 2/3 = –1/2 2/3
x x y x y
= x5/3 – (–1/2) y3 – 2/3

43. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN
For example, (2*3)2 = 22*32 = 36.
However the operation of taking power does not pass to terms.
For example, (2 + 3)2 ≠ 22 + 32.
In the example below, we use these rules to collect exponents.
Example B. Simplify the exponents.
2*1/3 2*3/2 1+2/3
x(x1/3y3/2)2 x*x2/3y3 x5/3y3
–1/2y2/3
= –1/2 2/3 = –1/2 2/3
x x y x y
= x5/3 – (–1/2) y3 – 2/3

44. Fractional Exponents
The operation of taking power may be passed to factors.
N N
The Power–Passing Rules: (AB) N =ANBN and ( A ) = A
B BN
For example, (2*3)2 = 22*32 = 36.
However the operation of taking power does not pass to terms.
For example, (2 + 3)2 ≠ 22 + 32.
In the example below, we use these rules to collect exponents.
Example B. Simplify the exponents.
2*1/3 2*3/2 1+2/3
x(x1/3y3/2)2 x*x2/3y3 x5/3y3
–1/2y2/3
= –1/2 2/3 = –1/2 2/3
x x y x y
= x5/3 – (–1/2) y3 – 2/3
= x5/3 +1/2 y7/3
= x13/6 y7/3

45. Review on Exponents and Power Equations
Power Equations

46. Review on Exponents and Power Equations
Power Equations
The solution to the equation
x 3 = –8 is
3
x = √–8 = –2.

47. Review on Exponents and Power Equations
Power Equations
The solution to the equation
x 3 = –8 is
3
x = √–8 = –2.
Using fractional exponent, we write these steps as
if x3 = –8

48. Review on Exponents and Power Equations
Power Equations
The solution to the equation
x 3 = –8 is
3
x = √–8 = –2.
Using fractional exponent, we write these steps as
if x3 = –8 then
The reciprocal of the power 3
x = (–8)1/3 = –2.

49. Review on Exponents and Power Equations
Power Equations
The solution to the equation
x 3 = –8 is
3
x = √–8 = –2.
Using fractional exponent, we write these steps as
if x3 = –8 then
The reciprocal of the power 3
x = (–8)1/3 = –2.

50. Review on Exponents and Power Equations
Power Equations
The solution to the equation
x 3 = –8 is
3
x = √–8 = –2.
Using fractional exponent, we write these steps as
if x3 = –8 then
The reciprocal of the power 3
x = (–8)1/3 = –2.
Rational Power equations are equations of the type xR = c
where R = P/Q is a rational number.

51. Review on Exponents and Power Equations
Power Equations
The solution to the equation
x 3 = –8 is
3
x = √–8 = –2.
Using fractional exponent, we write these steps as
if x3 = –8 then
The reciprocal of the power 3
x = (–8)1/3 = –2.
Rational Power equations are equations of the type xR = c
where R = P/Q is a rational number. To solve them, we take the
reciprocal power,

52. Review on Exponents and Power Equations
Power Equations
The solution to the equation
x 3 = –8 is
3
x = √–8 = –2.
Using fractional exponent, we write these steps as
if x3 = –8 then
The reciprocal of the power 3
x = (–8)1/3 = –2.
Rational Power equations are equations of the type xR = c
where R = P/Q is a rational number. To solve them, we take the
reciprocal power, that is,
if xR = c, or xP/Q = c

53. Review on Exponents and Power Equations
Power Equations
The solution to the equation
x 3 = –8 is
3
x = √–8 = –2.
Using fractional exponent, we write these steps as
if x3 = –8 then
The reciprocal of the power 3
x = (–8)1/3 = –2.
Rational Power equations are equations of the type xR = c
where R = P/Q is a rational number. To solve them, we take the
reciprocal power, that is,
if xR = c, or xP/Q = c Reciprocate the powers
then x = ( )c1/R or x = ( )cQ/P

54. Review on Exponents and Power Equations
Power Equations
The solution to the equation
x 3 = –8 is
3
x = √–8 = –2.
Using fractional exponent, we write these steps as
if x3 = –8 then
The reciprocal of the power 3
x = (–8)1/3 = –2.
Rational Power equations are equations of the type xR = c
where R = P/Q is a rational number. To solve them, we take the
reciprocal power, that is,
if xR = c, or xP/Q = c Reciprocate the powers
then x = ( )c1/R or x = ( )cQ/P
However, depending on the values of c and Q/P, it may be that
there is no real solutions, exactly one real solutions,
or both ( ) c1/R are real solutions.

55. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64

56. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64
x = 641/3 or that
3
x = √64 = 4.

57. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64
x = 641/3 or that
3
x = √64 = 4.
We note that this is the only solution.

58. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64
x = 641/3 or that
3
x = √64 = 4.
We note that this is the only solution.
b. x2 = 64

59. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64
x = 641/3 or that
3
x = √64 = 4.
We note that this is the only solution.
b. x2 = 64
x = 641/2 or that
x = √64 = 8.

60. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64
x = 641/3 or that
3
x = √64 = 4.
We note that this is the only solution.
b. x2 = 64
x = 641/2 or that
x = √64 = 8.
We note that both 8 are solutions.

61. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64
x = 641/3 or that
3
x = √64 = 4.
We note that this is the only solution.
b. x2 = 64
x = 641/2 or that
x = √64 = 8.
We note that both 8 are solutions.
c. x2 = –64

62. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64
x = 641/3 or that
3
x = √64 = 4.
We note that this is the only solution.
b. x2 = 64
x = 641/2 or that
x = √64 = 8.
We note that both 8 are solutions.
c. x2 = –64
x = (–64)1/2 so there is no real number solution.

63. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64
x = 641/3 or that
3
x = √64 = 4.
We note that this is the only solution.
b. x2 = 64
x = 641/2 or that
x = √64 = 8.
We note that both 8 are solutions.
c. x2 = –64
x = (–64)1/2 so there is no real number solution.
d. x –2/3 = 64

64. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64
x = 641/3 or that
3
x = √64 = 4.
We note that this is the only solution.
b. x2 = 64
x = 641/2 or that
x = √64 = 8.
We note that both 8 are solutions.
c. x2 = –64
x = (–64)1/2 so there is no real number solution.
d. x –2/3 = 64
x = 64–3/2
x = (√64)–3

65. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64
x = 641/3 or that
3
x = √64 = 4.
We note that this is the only solution.
b. x2 = 64
x = 641/2 or that
x = √64 = 8.
We note that both 8 are solutions.
c. x2 = –64
x = (–64)1/2 so there is no real number solution.
d. x –2/3 = 64
x = 64–3/2
x = (√64)–3 = 4–3 = 1/64.

66. Review on Exponents and Power Equations
Example C. Solve for the real solutions.
a. x3 = 64
x = 641/3 or that
3
x = √64 = 4.
We note that this is the only solution.
b. x2 = 64
x = 641/2 or that
x = √64 = 8.
We note that both 8 are solutions.
c. x2 = –64
x = (–64)1/2 so there is no real number solution.
d. x –2/3 = 64
x = 64–3/2
x = (√64)–3 = 4–3 = 1/64.
Again we check that both 1/64 are solutions.

67. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.

68. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1

69. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8

70. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4

71. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4
x = 43/2

72. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4
x = 43/2 = (41/2)3

73. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4
x = 43/2 = (41/2)3
x=8

74. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4
x = 43/2 = (41/2)3
x=8
b. 1 = 7 – 3(2x + 1)1/3

75. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4
x = 43/2 = (41/2)3
x=8
b. 1 = 7 – 3(2x + 1)1/3
3(2x + 1)1/3 = 7 – 1

76. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4
x = 43/2 = (41/2)3
x=8
b. 1 = 7 – 3(2x + 1)1/3
3(2x + 1)1/3 = 7 – 1 = 6

77. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4
x = 43/2 = (41/2)3
x=8
b. 1 = 7 – 3(2x + 1)1/3
3(2x + 1)1/3 = 7 – 1 = 6
(2x + 1)1/3 = 2

78. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4
x = 43/2 = (41/2)3
x=8
b. 1 = 7 – 3(2x + 1)1/3
3(2x + 1)1/3 = 7 – 1 = 6
(2x + 1)1/3 = 2
2x + 1 = 23

79. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4
x = 43/2 = (41/2)3
x=8
b. 1 = 7 – 3(2x + 1)1/3
3(2x + 1)1/3 = 7 – 1 = 6
(2x + 1)1/3 = 2
2x + 1 = 23
2x = 23 – 1 = 7

80. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4
x = 43/2 = (41/2)3
x=8
b. 1 = 7 – 3(2x + 1)1/3
3(2x + 1)1/3 = 7 – 1 = 6
(2x + 1)1/3 = 2
2x + 1 = 23
2x = 23 – 1 = 7
x = 7/2

81. Review on Exponents and Power Equations
For linear form of the power equations, we first isolate the term
with the power, then apply the reciprocal power to solve for x.
Example D. Solve for x.
a. 2x2/3 – 7 = 1
2x2/3 = 8
x2/3 = 4
x = 43/2 = (41/2)3
x=8
b. 1 = 7 – 3(2x + 1)1/3
3(2x + 1)1/3 = 7 – 1 = 6
(2x + 1)1/3 = 2
2x + 1 = 23
2x = 23 – 1 = 7
x = 7/2
We need calculators for irrational solutions which is our next
topic.