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Exponents Review
an means a multiplied by itself n times
Examples: 32 = 3∙3 = 9
(-5)3 = (-5)(-5)(-5) = -125
Evaluate
1. (-4)2
Exponent Rules
If m and n are rational numbers and no denominators are 0.
Zero Exponent: a0 = 1, for a ≠ 0
(A nonzero number raised to the 0 power equals 1.)
Examples: 50 = 1
(-2)0 = 1
Negative Exponent: a  n 
1
1
and  n  a n
n
a
a
1
1

2
81
9
Examples: 9 2 
1 2 7y2
y  5
x5
x
Rational Exponent: a  a  a
Example: 27 
2
3

3
m
n

 
n
m
4. 23∙2-5
5.
49
43
3
6.  1   1 
   
7 7
Simplify. Write all answers with positive
exponents.
4
10. x
x7
11. x5∙x-2
12. (3x4)2
am
Quotient Rule: n  a m  n
a
(Divide the same base, subtract the exponents.)
x9
 x 9 4  x 5
4
x
13. 2x0
14. (y4)-2
Power Rule: (am)n = am∙n
(Exponent raised to an exponent, multiply exponents.)
Example: (53)8 = 53∙8 = 524
Product Raised to a Power: (ab)n = anbn
(Raise each factor to the nth power)
Example: (7y)4 = 74y4 = 2401y4
n
an
a
Quotient Raised to a Power:    n
b
b
15.   5 x 2 
 3 
 y 
2 7
16. a b
(2b 2 )5
17. (-y-3)-2
18. (x1/2 y2)4
19. x1/2 x1/3
(Raise the numerator and denominator to the nth power)
3
4
1/ 2
2
Product Rule: am ∙ an = am+ n
(Multiply the same base, add the exponents.)
Example: x2 ∙ x7 = x2+ 7= x9
Example:
0
9.  16 
 
 25 
27  3  9
2
3.  3 
 
8
8. 641/2
7 x 5 y 2  7 
n
2. -42
7. (-3)2 + (-2)3
1
 23  8
3
2
m
Practice
x3
x3
 x
Example:    3 
512
8
8
3 / 4
20. y
y 7 / 4
2
1. 16
2. -16
3. 1
4.
1
4
5. 4096
6. 7
7. 1
8. 8
9.
10.
4
5
1
x3
11. x3
12. 9x8
13. 2
14. 1
y8
4
15. 25 x
y6
16.
a2
32b 3
17. y6
18. x2 y8
19. x5/6
20. y