1. 7-3 Multiplication Properties of Exponents
Hubarth
Algebra

2. Multiplying Powers With the Same Base
For every nonzero number a and integers m and n, 𝑎 𝑚 ∙ 𝑎 𝑛 = 𝑎 𝑚+𝑛 .
Example ∙ 3 4 = = (ℎ 2 ) ℎ 9 = ℎ 2+9 = ℎ 11

3. Ex 1 Multiplying Powers
Rewrite each expression using each base only once.
Add exponents of powers with the
same base.
73 + 2 = a.
73 • 72
= 75
Simplify the sum of the exponents.
Think of – 2 as (–2) to add the exponents.
– 2 = b.
44 • 41 • 4–2
= 43
Simplify the sum of the exponents.
Add exponents of powers with the
same base.
68 + (–8) = c.
68 • 6–8
= 60
Simplify the sum of the exponents.
Use the definition of zero as an exponent.
= 1

4. Ex 2 Multiplying Powers in an Algebraic Expression
Simplify each expression. a.
p2 • p • p5
Add exponents of powers
with the same base. p =
= p 8
Simplify.
2q • 3p3 • 4q4 b.
Commutative and
Associative Properties of
Multiplication
(2 • 3 • 4)(p3)(q • q 4) =
Multiply the coefficients.
Write q as q1.
= 24(p3) (q1• q 4)
Add exponents of powers
with the same base.
= 24(p3) (q1 + 4)
Simplify.
= 24p3q5

5. Ex 3 Multiplying Numbers in Scientific Notation
Simplify (3  10–3)(7  10–5). Write the answer in scientific notation.
Commutative and
Associative Properties of Multiplication
(3 • 7)(10–3 • 10–5)
(3  10–3)(7  10–5) =
= 21  10–8
Simplify.
= 2.1  101 • 10–8
Write 21 in scientific
notation.
= 2.1  (– 8)
Add exponents of
powers with the same
base.
= 2.1  10–7
Simplify.

6. Practice
Rewrite each expression using each base only once.
5 3 ∙ b. (2 4 )( 2 −3 ) c. 7 −3 ∙ 7 2 ∙ 7 6
2. Simplify each expression.
𝑛 2 ∙ 𝑛 3 ∙7𝑛 b. 2𝑦 3 ∙ 7𝑥 2 ∙ 2𝑦 4 c. (𝑚 2 ) 𝑛 −2 7𝑚
3. Simplify the expression. Write the answer in scientific notation.
(2.5 x )(6 x )
5 9
2 1 =2
7 5
7𝑛 6
28𝑥 2 𝑦 7
7𝑚 3 𝑛 2
1.5 x