Download 6.1 Exponent Rules

Algebra 2
6-1 Exponent Rules
Obj: able to multiply monomials and to simplify
expressions involving powers of monomials
Write the following without exponents, then simplify
1. (x3)(x2)
2. (d)(d2)
= ∙ ∙ ∙ ∙
Guidelines for simplifying exponents.
Assume that no variable is equal to zero.
1. No power of a power
2. Each base appears exactly once
3. No negative exponents
4. Fractions are simplified
(no decimal answers)
=
Power of a Product
3. (w3) (w2)
For any number a, and all integers m and n: (am )(an )=
4. (4b5) (1b3)
Write out the number of times the base in parentheses is used as a factor and simplify
5. (f 2)3
6. (g3)4
= ∙
∙
=
Power of a Power
7. (y5) 4
For any number a, and all integers m and n:
(am) n =
8. (23) 2
Write out the number of times the base in parentheses is used as a factor and simplify
9. (2x2)3
10. (4m5)2
=2 ∙ 2 ∙ 2
=
Power of a Monomial
11. (-2a2b3)2
For all numbers a and b, and all integers m, n, & p:
(ambn)p =
12.(4a2b3)4
Rewrite each numerator and denominator without exponents, then simplify. Assume all denominators are not
equal to zero.
13.
=
m5
14.
m3
Guidelines for simplifying exponents.
a7
Assume that no variable is equal to zero.
1. No power of a power
2. Each base appears exactly once
3. No negative exponents
4. Fractions are simplified
(no decimal answers)
a3
∙ ∙ ∙ ∙
∙ ∙
=
Quotient of Powers
For all integers m and n, and any nonzero number a:
am
an
15.
a 5b 7
16.
a 3b 2
Simplify using the quotient of powers rule
17.
d
18.
d3
y
5
Negative Exponents
d3
d3
20. 2x0
Simplify using the quotient of powers rule
y
d −6
For any nonzero number a : a0 =
19. (2x)0
3
d3
Write without exponents and simplify
3
Zero Exponent
21.
=
Write without exponents and simplify
22.
y3
y5
For any nonzero number a and any integer n:
a –n =
a −n
=
1
&
1
=
a −n
Simplify so that there are no negative exponents in your answer.
23.
w3
w
24.
8
x 2 y −3 z 4
x −3 z 6
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even if somebody is
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