Transcript 7-2 Multiplying Powers with the Same Base

7-2
Multiplying Powers
with the Same Base
You can write a product of powers with
the same base using one exponent.
𝑛
𝑚
𝑛+𝑚
𝑎 ∙𝑎 =𝑎
4
Example: 3
∙
2
3
= 3∙3∙3∙3 3∙
Problem 1: Multiplying Powers
What is each expression written using each
base only once:
4
• 12
•9
−3
∙
3
12
2
6
∙9 ∙9
Problem 2: Multiplying Powers in
Algebraic Expressions
When variable factors have more then one base, be
careful to combine only those powers with the same
base.
What is the simplified form of each expression?
5
4𝑧 ∙ 9𝑧
−12
What is the simplified form of
each expression?
4
2
• 2𝑎 ∙ 9𝑏 ∙ 3𝑎
3
2
• −4𝑐 ∙ 7𝑑 ∙ 2𝑐
−2
Problem 3: Multiplying with Scientific
Notation
Problem 4: Simplifying Expressions with
Rational Exponents
Simplify the expression:
1
4
• 81
1
3
• 27
1
2
• 64
3
2
You can also have expressions like 9 ,
which means
1
2
1
2
1
2
9 ∙ 9 ∙ 9 = 3 ∙ 3 ∙ 3 = 27
Problem 5: Simplifying Expressions with
Rational Exponents
Simplify each expression:
• 64
3
2
• 27
2
3
• 16
3
4
Problem 6: Simplifying Expressions with
Rational Exponents
Simplify the Expression:
2
3
• 2𝑎 ∙ 3𝑏
3
5
• 2𝑐 ∙ 2𝑐
1
5
1
4
1
3
𝑎 ∙ 5𝑏
1
2