2.3 Part 1: Product Power Rules of Exponents

2.3 Part 1: Product Power Rules of Exponents

EQ: How can you simplify expressions using the power rules of exponents?

Multiple Choice

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

• add
• subtract
• multiply
• divide

Multiple Choice

(x⁵)⁴

• x⁹

• x²⁰

• x

• x⁵⁴

Multiple Select

$$\left(4^2\right)^{-2}$$  

• $$\frac{1}{4^{-4}}$$  

• $$4^0$$  

• $$1$$  

• $$\frac{1}{256}$$  

Multiple Choice

(x^-3)⁴

• $$\frac{1}{x^{12}}$$  

• $$\frac{1}{x^{-12}}$$  

• x

• x¹²

Multiple Choice

(b³)⁸

• b¹¹

• 8b³

• b²⁴

• 24b

Multiple Choice

(b^-2)^-12

• b¹⁰

• b²⁴

• $$\frac{1}{b^{24}}$$  

• $$\frac{1}{b^{14}}$$  

Multiple Select

$$\left(x^0\right)^{25}$$  

• $$x^{25}$$  

• $$x^0$$  

• $$1$$  

• $$\frac{1}{x^{25}}$$  

Multiple Choice

(3y⁴)²

• 9y⁸

• 9y⁶

• 6y⁸

• 6y⁶

Multiple Choice

(2ab)³

• 8a³b³

• 2ab³

• 6a³b³

• 6ab

Multiple Choice

(5ab)^-3

• 8a³b³

• $$\frac{1}{15a^3b^3}$$  

• 125a³b³

• $$\frac{1}{125a^3b^3}$$  

Multiple Choice

$$\left(u^0v^{-1}\right)^{-1}$$  

• $$v$$  

• $$uv$$  

• $$\frac{1}{v}$$  

• $$\frac{v}{u}$$  

Multiple Choice

(3x⁴y⁵)²

• 9x⁸y¹⁰

• 6x⁸y¹⁰

• 3x⁸y¹⁰

• x⁸y¹⁰

Multiple Choice

$$\left(3x^4y^{-4}\right)^{-2}$$  

• $$9x^8y^8$$  

• $$\frac{y^8}{9x^8}$$  

• $$\frac{6x^2}{y^6}$$  

• $$6x^2y^6$$  

Multiple Choice

$$\left(4h^{-4}j^4k^2\right)^{-1}$$  

• $$\frac{h^4}{4j^4k^2}$$  

• $$\frac{-4h^4}{j^4k^2}$$  

• $$\frac{4j^3k}{h^5}$$  

• $$4^{-1}h^4j^{-4}k^{-2}$$  

Multiple Choice

(7a²)(5a⁶b)²

• 35a¹⁴b²

• 175a¹²b²

• 175a¹⁴b²

• 35a¹⁴b

Multiple Choice

(-4r³s⁵)⁰ (3b⁴c²d)

• 1
• -12b⁴c²d
• 3b⁴c²d
• 0

Multiple Choice

Simplify.
(x³ ⋅ y⁴ ⋅ z)³ ⋅ (x⁵ ⋅ y ⋅ z³)²

• x¹⁹y¹²z⁹
• x¹⁹ y¹⁴z⁹
• x¹³y¹⁰z⁹
• x²³y⁴²z¹¹