Multiplying/Dividing Exponents

Simplify using the 9 Laws of Exponents:

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• 
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According to exponent rules, when we divide powers we _______ the exponents.

• add

• subtract

• multiply

• divide

Evaluate the expression using the quotient rule.

• x¹³

• x⁵

• x³⁶

• x^-5

According to exponent rules, when we divide with exponents of the same base we _______ the exponents.

• add

• subtract

• multiply

• divide

Evaluate this expression using the quotient rule.

• 9⁵

• 9⁹

• 1⁵

• 9^-5

Billy was asked to solve 3⁵∙3⁴. He got 9²⁰. What error did he make?

• When he multiplies exponents, he is supposed to add the base and the exponent

• When he multiplies exponents, he is supposed to multiply the base and keep the exponents

• When he multiplies exponents, he is supposed to keep the base and add the exponents if the base is the same

• None of the above

Answer explanation

Billy was asked to solve 35∙34. He got 920. What error did he make?

He should have kept the base the same and added the exponents. Instead, he seems to have multiplied the bases together AND multiplied the exponents together.

 $3^4\cdot3^5$

$=3^{4+5}$
$=3^9$

According to exponent rules, when we multiply two powers with the same base we _______ the exponents.

Example: c⁶ ⋅ c⁴

• add

• subtract

• multiply

• divide

Answer explanation

According to exponent rules, when we multiply two powers with the same base we add the exponents.

Example:
$c^6\cdot c^4$
$=\left(c\cdot c\cdot c\cdot c\cdot c\cdot c\right)\left(c\cdot c\cdot c\cdot c\right)$

$=c\cdot c\cdot c\cdot c\cdot c\cdot c\cdot c\cdot c\cdot c\cdot c$
$=c^{6+4}\ =\ c^{10}$

• add

• subtract

• multiply

• divide

Answer explanation

According to exponent rules, when we divide two powers with the same base we subtract the exponents.

2³ * 2² 

• 2⁴

• 8⁴

• 36

• 2⁵

• 2y²⁴
• 2 / y¹⁰
• 2y¹⁰
• 2y¹⁴