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BASE OR NUMBER ISTHE NUMBER OF TIMES
MULTIPLIED BY ITSELF
2
2* 2* 2 =8
a number written as
a base number with an exponent
BASE EXPONENT
LIKE THIS:
2 SAY 2 TO THE 5th POWER
THE REPEATED FRACTION IN A
MULTIPLICATON PROBLEM
BASE = POWER
FACTOR * FACTOR * FACTOR = PRODUCT
2 * 2 * 2 = 8
jjj
34
means (3333)  81
(3)4
means (3)(3)(3)(3)  81
33
means (333)  27
(3)3
means (3)(3)(3)  27
2 SAY 2 TO THE 2ndPOWER OR
TWO SQUARED
MOST MATHEMATICIAN SAY TWO
SQUARED
2 = 2 2 = 4
2 SAY 2 TO THE 3rd POWER OR
TWO CUBED
MOST MATHEMATICIANS SAY
TWO CUBED
2 = 2 2 2 =8
THE BASE IS ANY NUMBER BUT 0,THE
ANSWER IS 1.
2 =1
4,638 =1
ANY NUMBER {except the number 0} =1
0 =UNDEFINED
THE ANSWER IS THE SAME
NUMBER AS THE BASE NUMBER
2 =2
4,638 =4,638
ANY NUMBER =THE SAME BASE
0 =0
THE EXPONENT 1 IS USUALY
INVISIBLE
xa
 xb
 xab
xa
) 3
 xab
xa
ya
(xy)a
PRODUCT OF POWERS
ADD THR EXPONENTS
POWE R TO A
POWERMUTIPLY THE EXPONENTS
POWER OF
PRODUCT
This property is used when dividing two or more
exponential expressions with the same base.
(x)(x)(x)
(x)(x)(x)(x)(x)
x3
x5

1
(x)(x)
  x2
1
x4
x4
x3
4

1

1

1
x3
x4
x7

1
 x x3x3
Q1}Evaluate the variable expression when x
= 1, y = 2, and w = -3 ?
(x)2
 (y)2
22
(x)  (y)
(1)2
 (2)2
14  5
Step
1
Step
2
Step
3
(x  y)2
(x  y)2
(1)  (2) )2
(3)2
 9
Step
1
Step
2
Step
3
wxy
wxy
(3)(1)2
Step
1
Step
2
Step
3
(3)(1)  3
17
MADE BY - ARJIT MITTAL
CLASS – 8B

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exponents and power

  • 1.
  • 2.
  • 3. BASE OR NUMBER ISTHE NUMBER OF TIMES MULTIPLIED BY ITSELF 2 2* 2* 2 =8
  • 4. a number written as a base number with an exponent BASE EXPONENT LIKE THIS: 2 SAY 2 TO THE 5th POWER
  • 5. THE REPEATED FRACTION IN A MULTIPLICATON PROBLEM BASE = POWER FACTOR * FACTOR * FACTOR = PRODUCT 2 * 2 * 2 = 8
  • 6. jjj
  • 7. 34 means (3333)  81 (3)4 means (3)(3)(3)(3)  81 33 means (333)  27 (3)3 means (3)(3)(3)  27
  • 8. 2 SAY 2 TO THE 2ndPOWER OR TWO SQUARED MOST MATHEMATICIAN SAY TWO SQUARED 2 = 2 2 = 4
  • 9. 2 SAY 2 TO THE 3rd POWER OR TWO CUBED MOST MATHEMATICIANS SAY TWO CUBED 2 = 2 2 2 =8
  • 10. THE BASE IS ANY NUMBER BUT 0,THE ANSWER IS 1. 2 =1 4,638 =1 ANY NUMBER {except the number 0} =1 0 =UNDEFINED
  • 11. THE ANSWER IS THE SAME NUMBER AS THE BASE NUMBER 2 =2 4,638 =4,638 ANY NUMBER =THE SAME BASE 0 =0 THE EXPONENT 1 IS USUALY INVISIBLE
  • 12. xa  xb  xab xa ) 3  xab xa ya (xy)a PRODUCT OF POWERS ADD THR EXPONENTS POWE R TO A POWERMUTIPLY THE EXPONENTS POWER OF PRODUCT
  • 13. This property is used when dividing two or more exponential expressions with the same base. (x)(x)(x) (x)(x)(x)(x)(x) x3 x5  1 (x)(x)   x2 1 x4 x4 x3 4  1  1  1 x3 x4 x7  1  x x3x3
  • 14.
  • 15.
  • 16.
  • 17. Q1}Evaluate the variable expression when x = 1, y = 2, and w = -3 ? (x)2  (y)2 22 (x)  (y) (1)2  (2)2 14  5 Step 1 Step 2 Step 3 (x  y)2 (x  y)2 (1)  (2) )2 (3)2  9 Step 1 Step 2 Step 3 wxy wxy (3)(1)2 Step 1 Step 2 Step 3 (3)(1)  3
  • 18. 17 MADE BY - ARJIT MITTAL CLASS – 8B