Properties of Exponents

Lesson: Properties of Exponents

An overview of the basic exponent properties

Product Rule

Multiple Choice

Simplify

$$x^3y^4\left(x^2y^2\right)$$  

• $$x^6y^6$$  

• $$x^5y^6$$  

• $$x^5y^8$$  

• $$x^6y^8$$  

Quotient Rule

Multiple Choice

Simplify

$$\frac{x^7y^5}{xy^2}$$  

• $$x^6y^7$$  

• $$x^8y^7$$  

• $$x^7y^{10}$$  

• $$x^6y^3$$  

Power Rule

Multiple Choice

Simplify

$$\left(x^4\right)^6$$  

• $$x^{10}$$  

• $$x^{-2}$$  

• $$x^2$$  

• $$x^{24}$$  

Power of a Product Rule (Distributive Rule)

Multiple Choice

Simplify

$$\left(3a^2c\right)^3$$  

• $$9a^6c^3$$  

• $$27a^5c^3$$  

• $$27a^6c^3$$  

• $$9a^5c^3$$  

Power of a Quotient Rule (Distributive Rule)

Multiple Choice

Simplify

$$\left(\frac{x^4}{y^5}\right)^3$$  

• $$\frac{x^7}{y^8}$$  

• $$\frac{x^{12}}{y^{15}}$$  

• $$\frac{x^7}{y^{15}}$$  

• $$\frac{x^{12}}{y^8}$$  

Zero Exponent Rule

Multiple Choice

Simplify

$$m^0$$  

• 1

• 0

• m

• 1m

Negative Exponents

Multiple Choice

Simplify

$$x^2y^{-3}$$  

• $$\frac{y^{-3}}{x^2}$$  

• $$\frac{x^2}{y^3}$$  

• $$\frac{y^3}{x^{-2}}$$  

• $$\frac{y^3}{x^2}$$