Quotient of Powers

Power of Power with Quotient Property

By Scott Donnelly

Multiple Choice

Simplify

$$3^8\cdot3^6$$  

• $$3^{48}$$  

• $$3^2$$  

• $$3^{14}$$  

• $$9^{48}$$  

Multiple Choice

Simplify

$$\frac{x^3}{x^{10}}$$  

• $$\frac{0}{x^7}$$  

• $$x^7$$  

• $$\frac{1}{x^7}$$  

• $$x^{13}$$  

Multiple Choice

Simplify

$$\left(2^6x^4y\right)^7$$  

• $$2^{13}x^{11}y$$  

• $$2^{13}x^{10}y^8$$  

• $$2^{42}x^{28}y$$  

• $$2^{42}x^{28}y^7$$  

​Quotient Property

If we have a power outside of a parenthesis, we distribute the power to everything INSIDE the parenthesis.

Quotient Property

Example

Quotient Property

Example

Multiple Choice

Simplify

$$\left(\frac{2^3x^4}{3^8}\right)^2$$  

• $$\frac{2^5x^6}{3^{10}}$$  

• $$\frac{2^6x^8}{3^8}$$  

• $$\frac{2^6x^8}{3^{16}}$$  

Common Base

If there is a common base inside parenthesis, combine those first then distribute.

Example

Example

Multiple Choice

Show out work on dry erase boards,

$$\left(\frac{3^2x^4}{3^5x}\right)^2$$  

• $$\frac{x^6}{3^6}$$  

• $$3^6x^6$$  

• $$\frac{3^6}{x^6}$$  

Multiple Choice

Show out work on dry erase boards,

$$\left(\frac{5x^4}{10x}\right)^8$$  

• $$2x^{24}$$   

• $$\frac{x^{24}}{2}$$   

• $$\frac{x^{24}}{2^8}$$