Product of Powers Lesson

1.2 Product and Quotient Rules of Exponents


Learning Target: Students will use the Laws of Exponents to multiply and divide monomials.

Team Time

Multiple Choice

Write an equivalent expression: $$12^4\times12^6$$  

• $$12^{10}$$  

• $$12^{24}$$  

• $$144^{10}$$  

• $$24^{10}$$  

Multiple Choice

What is the EXPONENT in the power written below?

4

• 0

• 4

• 1

• 2

Multiple Choice

Simplify:

$$t^9\cdot t^8$$  

• $$t^1$$  

• $$t^{72}$$  

•   $$t^{17}$$  

• None of the above

Multiple Choice

Find the missing exponent:

$$3^{16}=3^8\cdot3^?$$  

• 2

• 8

• 4

• 1

Multiple Choice

The Product of Powers Property says when the base is the same and the exponent is different you should ________________________

• add the bases

• multiply the bases

• add the exponents

• multiply the exponents

Multiple Choice

Simplify:

$$7^8\cdot7$$  

•   $$7^9$$  

•   $$49^8$$  

• $$7^8$$  

• None of the above

Multiple Choice

True or False $$7\times7^{8\ }$$   is equivalent to  $$7^4\times7^5$$  

• True 

• False 

Team Time

​You do:

​You do:

Multiple Choice

Division Law states: keep the base the same and do this to the exponents.

• multiply
• add
• subtract
• divide

Multiple Choice

15⁹÷15^{3 =}

• 15⁶
• 15¹²
• 1⁶
• 1¹²

Multiple Choice

Evaluate this expression using the quotient rule.

• 9⁵
• 9⁹
• 1⁵
• 9^-5

Multiple Choice

Evaluate the expression using the quotient rule.

• 1²²
• 1³⁰
• 6²²
• 6³⁰

Multiple Choice

Evaluate the expression using the quotient rule.

• 2¹⁴ z¹³
• 2²/z⁷
• 2¹⁴/ z⁷
• 2² z⁷

Multiple Choice

True or False: 

• True 
• False

Multiple Choice

Simplify the expression.

• 7⁶
• 7^-5
• 1/7⁵
• 7⁵

Multiple Choice

Simplify the expression. Write your answer as a power.

$$\frac{9^8}{9^2}$$  

• $$9^4$$  

• $$9^6$$  

• $$9^{10}$$  

• $$9^{16}$$  

Multiple Choice

Simplify the expression. Write your answer as a power.

$$\frac{h^{10}}{h^3}$$  

• $$h^7$$  

• $$h^{13}$$  

• $$h^{\frac{10}{3}}$$  

• $$h^{30}$$  

Multiple Choice

Simplify the expression. Write your answer as a power.

$$\frac{\left(-2\right)^9}{\left(-2\right)^4}$$  

• $$-2^5$$  

• $$\left(-2\right)^{13}$$  

• $$\left(-2\right)^{36}$$  

• $$\left(-2\right)^5$$  

Multiple Choice

Simplify the expression. Write your answer as a power.

$$\frac{\left(1.5\right)^{12}}{\left(1.5\right)^2}$$  

• $$\left(1.5\right)^6$$  

• $$\left(1.5\right)^4$$  

• $$\left(1.5\right)^{14}$$  

• $$\left(1.5\right)^{10}$$  

Multiple Choice

Simplify the expression. Write your answer as a power.

$$\frac{b^7\cdot b\cdot b^5}{b^{10}}$$  

• $$b^2$$  

• $$b^{23}$$  

• $$b^{13}$$  

• $$b^3$$