Exponent Rules

Exponent Rules

By Rebecca Hasbrouck

Exponent Rules Overview

Match

Match the exponent rules. Watch the video to help you if you are stuck.

• $$x^ax^b$$

• $$\frac{x^a}{x^b}$$

• $$x^0$$

• $$x^{-a}$$

• $$\left(x^a\right)^b$$

• $$x^{a+b}$$

• $$x^{a-b}$$

• $$1$$

• $$\frac{1}{x^a}$$

• $$x^{ab}$$

Rule 2: The Product Rule

Multiple Choice

Simplify:

$$h^2\cdot h^6$$  

• $$h^8$$  

• $$h^4$$  

• $$h^{12}$$  

• $$h^{-4}$$  

Multiple Choice

Simplify:

$$\left(-2a^2b\right)\cdot\left(7a^3b\right)$$  

• $$5a^3b^2$$  

• $$-14a^5b^2$$  

• $$-14a^5b$$  

• $$-14a^6b^2$$  

Draw

Complete the following product rule questions

Rule 3: The Power Rule

Multiple Choice

Simplify:

$$\left(x^4\right)^5$$  

• $$x^{20}$$  

• $$x^9$$  

• $$x^{12}$$  

• $$x^{-1}$$  

Multiple Choice

Simplify:

$$\left(-2m^5\right)^2$$  

• $$-4m^7$$  

• $$-4m^{10}$$  

• $$4m^7$$  

• $$4m^{10}$$  

Draw

Complete the following power to a power rule questions

Rule 4: The Quotient Rule

Multiple Choice

Simplify:

$$\frac{\left(y^2\right)^3}{y^4}$$  

• $$y^2$$  

• $$y$$  

• $$y^{12}$$  

• $$y^{10}$$  

Multiple Choice

Simplify:

$$\frac{27x^6}{9x}$$  

• $$3x^7$$  

• $$3x^5$$  

• $$3x^6$$  

• $$3x^4$$  

Draw

Complete the following quotient rule questions

Rule 6: The Negative Exponent Rule

Multiple Choice

Simplify:

$$-5x^{-2}$$  

• $$\frac{1}{5x^2}$$  

• $$5x^2$$  

• $$\frac{-5}{x^2}$$  

• $$\frac{1}{-5x^2}$$  

Multiple Choice

Simplify:

$$\frac{4k^2}{8k^4}$$  

• $$\frac{1}{2k^2}$$  

• $$\frac{2}{k^2}$$  

• $$\frac{1}{2k^6}$$  

• $$\frac{k^{-2}}{2}$$  

Rule 7: The Zero Exponent Rule

Multiple Choice

Simplify:

$$7x^0$$  

• 1

• 0

• 7

• 7x

Multiple Choice

Simplify:

$$\frac{w^8}{w^8}$$  

• 1

• $$w^0$$  

• $$w^8$$  

• $$w^{16}$$  

Draw

Complete the following negative and zero exponent rules questions.