Quotient Rules

Quotient Rules

By Scott Donnelly

Multiple Choice

Simplify

$$5^3\cdot5\cdot5^4$$  

• $$5^7$$  

• $$5^8$$  

• $$5^{13}$$   

• $$125^8$$  

Multiple Choice

When simplifying the exponents below, what do we do with the powers?

$$5^3\cdot5\cdot5^4$$  

• Add

• Subtract

• Multiply

Quotient Property

​Rules

When we multiply the powers, we add them.

When dividing the exponents we subtract the powers.​

The BASE DOES NOT change and we only combine like bases.​

Example

Example

Multiple Choice

Simplify $$\frac{4^6}{4^3}$$  

• $$4^9$$  

• $$4^3$$  

• $$1^3$$  

Multiple Choice

Simplify $$\frac{3^5x^6y^3}{3^3xy^2}$$  

• $$3^2x^5y$$  

•   $$1x^7y^5$$  

• $$3^8x^7y^5$$  

Quotient Rule

Quotient Rule

Multiple Choice

Simplify $$\frac{5^2}{5^4}$$  

• $$5^2$$  

• $$\frac{1}{5^2}$$  

• $$5^6$$  

Multiple Choice

Simplify $$\frac{3x^7}{3^8x^5}$$  

• $$\frac{1x^{12}}{3^7}$$  

• $$\frac{1x^2}{3^7}$$  

• $$3^7x^2$$  

Example

Multiple Choice

Simplify $$\frac{10x^5}{20x^4}$$  

• $$2x$$  

• $$\frac{x}{2}$$  

• $$\frac{x^9}{2}$$