5.2 - 5.3 Law of Exponents - Power to a Power

Use multiplication properties of
exponents to evaluate and simplify
expressions.

Objective

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A number or variable written without an exponent
actually has an exponent of 1.

Remember!

10 = 101

y = y1

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To find a power of a power, you can use the
meaning of exponents.

Notice the relationship between the exponents in
the original power and the exponent in the final
power:

Powers of products can be found by using the
meaning of an exponent.

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Multiple Choice

Which property rule does this expression follow?

$$5^2\ \cdot\ 5^8$$

• Product of Powers 

• Power of Powers

Multiple Choice

Which property rule does this expression follow? 

$$\left(7^5\right)^2$$  

• Product of Powers 

• Power or Powers

Multiple Choice

Simplify the expression

$$\left(12^2\right)^4$$  

• $$12^6$$  

• $$12^8$$  

Multiple Choice

Simplify the expression

$$12^4\cdot12^{15}$$  

• $$12^{19}$$  

• $$12^{60}$$  

Multiple Choice

Simplify the expression

$$\left(52^5\right)^4$$  

• $$52^9$$  

• $$52^{20}$$  

Multiple Choice

Simplify:
(xy²)⁴

• x⁴y²

• x⁴y⁸

• x³y²

• x⁵y⁶

Multiple Choice

(r⁴)⁶

• 10r

• r¹⁰

• 24r

• r²⁴

Multiple Choice

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

• add

• subtract

• multiply

• divide

Multiple Choice

Simplify: (3x²)³

• 27x⁶

• 9x⁶

• 3x⁶

• 9x⁵

Multiple Choice

(2x³y)⁶

• 2x¹⁸y⁶

• 64x¹⁸y⁶

• 64x³y⁶

• 2x³y⁶

Multiple Choice

(4p³q⁶)⁴

• 4p¹²q²⁴

• 256p⁷q¹⁰

• 256p¹²q²⁴

• 4p⁷q¹⁰