8th Power to a Power Property of Exponents

8th Power to a Power Property of Exponents

By Jen D'Aiuto

​Quick Review..Zero and Negative Exponent Properties

​(3n³)⁰ =

​

​

n^-4 =

​

​

1​ =

x^-5 ​

​

​7y⁰ =

​

​

​6a³b^-2 =

​

​

​1 =

​3y^-2

Multiple Choice

(m³n⁴)⁰ =

• 1

• 0

• m³n⁴

Multiple Choice

x^-5 =

• x⁵

• 1

  x⁵

• 1

  x^-5

Multiple Choice

7m^-3n⁶ =

• 7n³

• n⁶

  7m³

• 7n⁶

  m³

​Quick Review..Multiplication Exponent Property

​y³ ⋅ y⁷ =

​

​

​

8n^-4 ⋅ 3n⁶ =

​

​

​

​

​3n³ ⋅ 5n² =

​

​

​

6x³ ⋅ 4x^-7 =

​

​

​

Multiple Choice

m⁵ ⋅ m⁶

• m¹¹

• m

• m³⁰

Multiple Choice

4m^-4 ⋅ 2m⁶

• m^-2

• 8m¹⁰

• 8m²

​

To find the power of a power, multiply the exponents.

​Power to a Power Property of Exponents

​(b^m)ⁿ = b^mn

​Power to a Power w/Numbers

(5⁴)³ = 5³⁽⁴⁾ = 5¹²​

Expanded:

​(5⁴)³ = 5⁴ ⋅ 5⁴ ⋅ 5⁴

= 5⁴⁺⁴⁺⁴

⁼ 5¹²​

Try these...

​

(7⁴)³ =

​

(8²)^-5 =​

Multiple Choice

$$\left(7^2\right)^3$$  

• $$7^5$$  

• $$7^6$$  

Multiple Choice

5⁸ ⋅ 5³

•  5¹¹

• 5²⁴ 

​Power to a Power w/Variables

(x⁵)² = x⁵⁽²⁾ = x¹⁰​

Expanded:

​(x⁵)² = x⁵ ⋅ x⁵

= x⁵⁺⁵

⁼ x¹⁰​

Try these...

​

(x³)⁵ =

​

(y⁴)^-2 =​

Multiple Choice

(n⁴)⁵

• n⁹

• n²⁰

Multiple Choice

(x^-3)²

• x⁶

• 1

  x⁶

• x^-1

​Power to a Power Practice

(7x⁵)² = 7² ⋅ x⁵⁽²⁾ = 49x¹⁰​

Try these...

​

(2x²)⁵ =

​

(3y³)² =​

Multiple Choice

(4n³)⁵

• 4n⁸

• 4n¹⁵

• 4⁵n¹⁵

• 4⁵n⁸

​Power to a Power Practice w/Negative Exponents

(6x^-4)³ = 6³ ⋅ x^-4(3) = 216x^-12

​= 216

Try these...

​

(4x^-2)⁵ =

​

(7y³)^-2 =​

​

​(5m^-3n⁴)^-2 =​

​

​x¹²

Multiple Choice

(3p^-2)⁴

• 3p^-8

• 3p²

• $$\frac{3^4}{p^8}$$  

• 3⁴p⁸

Multiple Choice

(4m²n^-4)^-3

• n¹²

  4³m⁶

• 4n¹²

  m⁶

• 4³

  m⁶n¹²

• 4³m⁶n¹²

Multiple Choice

(4x²y^-4 ⋅ 2xy⁵)³

• 8³x⁶y³

• 6³x⁹y³

• 8³x⁹y³