Power of a Quotient

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

• multiply
• add
• subtract
• divide

(5²)³

• 5⁶
• 5⁵
• 5⁷
• 5⁸

True or False?

• True
• False

3.) Simplify

(45x⁶y⁹) ÷ (5x⁴y²)

• 9x²y⁷

• 40x²y⁷

• 9x²/y⁷

• 9x¹⁰y¹¹

Tags

CCSS.HSA.APR.A.1

Which of the following is the correct way to simplify this expression?
 $\left(a^mb^n\right)^p$  

•  $ab^{m\cdot n\cdot p}$  
  

•  $a^{m\cdot p}\ b^{n\cdot p}$  

•  $a^mb^n$  
  

What's our "shortcut" for thinking of this property?
 $\left(a^mb^n\right)^p\ =\ a^{mp}\ b^{np}$  

• It's like "distributing" the power

• We add the powers together

• We divide the powers

Simplify the following:
 $\left(r^7s^3\right)^3$  

•  $r^7s^9$  

•  $r^{21}s^9$  

•  $r^{21}s^3$  

Simplify the following:
 $\left(abc^5\right)^5$ 

•  $a^5b^5c^{25}$ 

•  $a^5b^5c^5$ 

•  $abc^{25}$ 

Simplify the following:
$\left(4x^3y^2\right)^2$

• $16x^3y^2$

• $4x^6y^4$

• $16x^6y^4$

Which of the following is the correct way to simplify this expression?
 $\left(\frac{a^m}{b^n}\right)^p$  

•  $\frac{a^{m\cdot p}}{b^{n\cdot p}}$  
  

•  $\frac{a^m+a^p}{b^n+b^p}$  

•  $a^{m\cdot p}\ b^{n\cdot p}$