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Lesson 8.1 Apply Exponent Properties Involving Products After today’s lesson, you should be able to use properties of exponents involving products to simplify expressions. (CA 2.0)
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Lesson 8.1 Apply Exponent Properties Involving Products
After today’s lesson, you should be able to use properties of exponents involving products to
simplify expressions. (CA 2.0)
Powers
A power is an expression that represents repeated multiplication of the same factor.
Writing a Power
A power can be written in a form using a base and an exponent.
Examples:
The power is , the base is 3 and the exponent is 4.
Examples:
2)
The power is , the base is x and the exponent is 2.
Examples:
3)
The power is , the base is 5x and the exponent is 2.
Multiplying powers with the same base
Simplify by writing each expression in expanded form. Write your answer using exponents.
Ex. 4)
Multiplying powers with the same base
Simplify by writing each expression in expanded form. Write your answer using exponents.
Ex. 5)
Product of Powers Property
Rule: Product of Powers
Words: To multiply powers having the same base, add the exponents.
Algebra:
Examples: Simplify the expression. Write your answer using exponents.
6)
Examples: Simplify the expression. Write your answer using exponents.
7)
Examples: Simplify the expression. Write your answer using exponents.
8) You Try
Finding a power of a power
Simplify by writing each expression in expanded form. Write your answer using exponents.Ex 9)
Finding a power of a power
Simplify by writing each expression in expanded form. Write your answer using exponents.Ex. 10)
Power of a Power Property
Rule: Power of a Power
Words: To find a power of a power, multiply exponents.
Algebra:
Examples: Simplify the expression. Write your answer using exponents.
11)
Examples: Simplify the expression. Write your answer using exponents.
12)
Examples: Simplify the expression. Write your answer using exponents.
13)
Examples: Simplify the expression. Write your answer using exponents.
14) You Try
Finding a power of a product
Simplify by expanding. Write your answer using exponents.Ex. 15)
Finding a power of a product
Simplify by expanding. Write your answer using exponents.Ex. 16)
Power of a Product Property
Rule: Power of a Product
Words: To find a power of a product, find the power of each factor and then multiply.
Algebra:
Example: Simplify the expression. Write your answers using exponents.
17)
Example: Simplify the expression. Write your answers using exponents.
18)
Example: Simplify the expression. Write your answers using exponents.
19)
Example: Simplify the expression. Write your answer using exponents.
20) You Try
Combining methods:Examples: Simplify the expression.
21)
Combining methods:Examples: Simplify the expression.
22) You Try
