Powers & Exponents Notes
A ____________________ is the product of repeated factors. It uses a ________________ and an
_______________________ and has the form:
bx
The __________________ is the common factor. The _______________________tells how many times the
_______________________ is used as a factor.
Example 1: Write the following expressions using exponents:
(−2) ∙ (−2) ∙ (−2) ∙ 3 ∙ 3 ∙ 3 ∙ 3 =
1 1 1 1
∙ ∙ ∙ =
2 2 2 2
m∙m∙n∙n∙m=
Example 2: Evaluate each expression.
25 ∙ 7 =
−(2⁄3)4 =
Example 3: Evaluate each expression if 𝒂 = 𝟑 and 𝒃 = 𝟓.
𝑎2 + 𝑏 4 =
(𝑎 − 𝑏)2 =
Properties of Exponents
Multiplying Powers:
To multiply powers with the same base, keep the base the same and ____________ the exponents.
Example:
____• ____ = _______
x5x3 =
Dividing Powers:
To divide powers with the same base, keep the base the same and ________________the exponents.
= _______
______
Example:
_x9 =
x5
Power of a Power
To find a power of a power, keep the base the same and ___________________the exponents.
Example:
(_____)
= _______
(x4)3 =
Product to a power:
To raise a product to a power, ____________________ the power to each factor.
Example:
(_____)
= _______
(4x3)2=
Quotient to a power
To raise a quotient to a power, ___________________ the power to the numerator and the denominator.
Example:
2
𝑥5
.(
)
𝑦3
= _______
𝑥5
y(
)
𝑦3
2
Zero Exponent:
Any nonzero number raised to the “zero power” is equal to ______.
Example:
______
= _______
x0
Negative exponent:
Negative exponents indicate reciprocation; “_____________ “ and make the exponent positive.
Example One:
______
= _______
______
= _______
x-3
Example Two:
_1_
x-5