Study Guide Algebra I
Zero, Negative Exponents and Multiplying Powers
Chapter 8, sections 1, 3 & 4, pages 430-451
Know the exponent rules and be able to use them.
a m • a n = a m+n
(ab) n = a n b n
(a n ) m = a nm
a0 = 1
1
a−n = n
a
€ 1. Be able to simplify expressions or numbers raised to the zero power
REMEMBER: anything to the zero power is 1
150 = 1
-(8x)0 = -1  (8x)0 = 1 but the – sign is not raised to the 0 power
 4 0
−  = 1
 3
€ 2. Be able to simplify expressions or numbers to the negative power
REMEMBER: a negative exponent on the top goes to the bottom and becomes
positive and a negative exponent on the bottom goes to the top and becomes
positive.
Examples:
1.)
€
m 2 n −3
the m2 stays on the top because it’s exponent is +
the n-3 goes to the bottom because it’s exponent is –
m 2 n −3 =
1 1
2.) € 3−2 = 2 =
3€ 9
€
3.)
9−1
m2
NOTE: the negative goes away when you move it.
n3
move the 32 to the bottom
flip the fraction because they are both negative exponents
3−2
9−1
−2
3
32
9
= 1 = =1
9
9
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4.)
€
7s0 t −5
−1
2 m
the 7 & s0 stay on the top (positive exponents) and the m2
2
stays on the bottom (positive exponents)
−5
the t goes to the bottom and the 2−1 and goes to the top
(negative exponents)
€
7s0 t −5
7 •1• 2
14
= 2 5 = 2 5
−1 2€
2 m
m t
m t
€
REMEMBER: s0 = 1
€ 3. Be able to simplify power to power expressions using the exponent rules
Simplify the following expressions:
1.)
(−2m−5n)−2
1
€
(−2m−5n) 2
1
2
(−2) m
€
m10
4n 2
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2.)
€
€
−10 2
(5a 3b 2 ) 3
n
negative exponent (-2) moves the entire
expression to the denominator
multiply exponents
square (-2) & move the m
−10
to the top
5 3 a 3•3b 2•3
75a 9b 6
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€ 3.)
€
€
€
€
€
€
distribute the exponent 3 to each element
(2a−2b 3 ) 2 (ab 2 ) 3
2 2 a−2•2b 3•2 a1•3b 2•3
4a−4 b 6 a 3b 6
4a−4 a 3b 6b 6
4a−1b12
4b12
a
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distribute the exponents 2 & 3
multiply the exponents
rearrange terms
add your exponents
move a−1 to the denominator