exponents and power presentation for class 7&8.

1. NAME – ABCD
CLASS -7A
TOPIC -EXPONENTS AND
POWER

3. OBJECTIVE:
The students will simplify
expressions by using the
laws of exponents.

4. Intro to
Exponents
Learn to evaluate
expressions with
exponents.

5. HISTORY of the word
EXPONENT.
• The term EXPONENT
was introduced by
Michael Stifel (1487-
1567) in 1544 in
Arithmetica integra.

6. Review
Find the product.
6251. 5 • 5 • 5 • 5
2. 3 • 3 • 3
3. (–7) • (–7) • (–7)
4. 9 • 9
27
–343
81

7. The term 27
is called a power.
If a number is in exponential
form, the exponent
represents how many times
the base is to be used as a
factor.
7
ExponentBase
2

8. Identify how many
times 4 is a factor.
4 • 4 • 4 • 4 = 44
Write in exponential form.
A. 4 • 4 • 4 • 4
Identify how many
times d is a factor.
d • d • d • d • d = d5
B. d • d • d • d • d
Read 44
as “4 to the 4th
power.”
Reading Math

10. Identify how many
times –6 is a factor.
(–6) • (–6) • (–6) = (–6)3
Identify how many
times 5 is a factor.
5 • 5 = 52
C. (–6) • (–6) • (–6)
D. 5 • 5
Write in exponential form.
Remember to keep the – sign inside the ( )!
If it is outside, your answer will be negative
even if you have an even number of – signs.

11. Exponential Rule:Exponential Rule:
( )
nm mn
x x=
( )
23 3 2 6
Example: 4 4 4×
= =
( ) ( ) ( ) ( )
2 23
6
Proof: 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4
= × × = × × × × × =
= × × × × × =

12. 15
5•3
53
4
4
)4(
=
=
NOTE:
Multiply the exponents, not add them!
Words Numbers Algebra
To multiply
power of a
power, keep the
base and
multiply the
exponents.
Multiplying Power of a Power
(pr
)s
=
pr
• s
15
5•3
53
4
4
)4(
=
=

13. Identify how many
times x is a factor.x • x • x • x • x = x5
Write in exponential form.
A. x • x • x • x • x
Identify how many
times d is a factor.
d • d • d = d3
B. d • d • d

16. A. 35
= 243
35
= 3 • 3 • 3 • 3 • 3
Find the product of
five 3’s.
= –243
= (–3) • (–3) • (–3) • (–3) • (–3)(–3)5
Find the product of five –3’s.B. (–3)5
Always use parentheses to raise a negative
number to a power.
Helpful Hint
Evaluate.

17. C. 74
= 2401
74
= 7 • 7 • 7 • 7
Find the product of four 7’s.
= –729
= (–9) • (–9) • (–9)(–9)3
Find the product of three –9’s.D. (–9)3
Evaluate.

18. Simplifying Expressions
= 47
Simplify (25
– 32
) + 6(4)
= (32 – 9) + 6(4)
= (23) + 6(4)
= 23 + 24
Evaluate the exponents.
Subtract inside the parentheses.
Multiply from left to right.
Add from left to right.

19. = –49
Simplify (32
– 82
) + 2 • 3
= (9 – 64) + 2 • 3
= (–55) + 2 • 3
= –55 + 6
Evaluate the exponents.
Subtract inside the parentheses.
Multiply from left to right.
Add from left to right.