Download 7-4 Division Properties of Exponenets

7-4
Division Properties
of Exponents
Dividing Powers With the Same Base
• To divide powers with the same
base, subtract the exponents.
𝑎𝑚
𝑎𝑛
𝑚−𝑛
=𝑎
, where 𝑎 ≠ 0, and m and
n are rational numbers
Problem 1: Dividing Algebraic Expressions
What is the simplified form of each
expression?
•
•
5
𝑥2
𝑥2
𝑚2 𝑛4
𝑚5 𝑛3
Problem 2: Dividing Numbers in Scientific
Notation
Simplify each quotient. Write each
answer in scientific notation.
7
1.21 × 10
4.81 × 105
Simplify each quotient. Write each
answer in scientific notation.
6
7.33 × 10
4.33 × 104
Raising a Quotient to a Power
• To raise a quotient to a power, raise
the numerator and denominator to
the power and simplify
𝑛
𝑎
𝑏
𝑎𝑛
,
𝑛
𝑏
=
where 𝑎 ≠ 0, 𝑏 ≠ 0, and n
is a rational number
Problem 3: Raising a Quotient to a Power
What is the simplified form:
•
•
2
𝑧3
3
5
4 2
𝑥3
𝑎
𝑏
−𝑛
𝑏
=
𝑎
𝑛
Problem 4: Simplifying an Exponential
Expression
What is the simplified form?
•
•
2𝑥 6
−3
𝑦4
−2
𝑎
5𝑏