Study Guide and Intervention (continued) - MathnMind

8-2
Negative Exponents Any nonzero number raised to the zero power is 1; for example,
(0.5) 0 1. Any nonzero number raised to a negative power is equal to the reciprocal of the
number raised to the opposite power; for example, 63 1
. These definitions can be used
63 to simplify expressions that have negative exponents.
Zero Exponent For any nonzero number a, a0 1.
Negative Exponent Property For any nonzero number a and any integer n, an and an 1 1
.
an an The simplified form of an expression containing negative exponents must contain only
positive exponents.
Example
4a
Simplify . Assume that the denominator is not equal to zero.
3b6
16a2b6c5 Group powers with the same base.
(a3 2 )(b6 6 )(c5 b 1
c5 1
)
4
Quotient of Powers and Negative Exponent Properties
6 a
b6 3
4a 4
16 a2 3b6
16a2b6c5 a5b0c5 1
4
(1)c5 1 1
4 a5 Simplify.
c
Simplify.
5
4a5 The solution is . 4a5 Exercises
Negative Exponent and Zero Exponent Properties
Simplify. Assume that no denominator is equal to zero.
2 2
m
1. 2. 3.
23 m4 (x
4. 5. 6.
1y) 0
b
4
b5 (6a
7. 8. 9.
1b) 2
x
(b2 ) 4
4y0
x2 s3t5
(s2t3 ) 1
NAME ______________________________________________ DATE ____________ PERIOD _____
Study Guide and Intervention (continued)
Dividing Monomials
c 5
4w 1 y 2
4m2n2
8m1 10. 11. 0
(a 2 b 3 ) 2
(ab) 2
(3st) 2 u 4
s 1 t 2 u 7
12. (2mn2 ) 3
4m 6 n 4
© Glencoe/McGraw-Hill 462 Glencoe Algebra 1
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