Powers of Products and Quotients

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

•  $ab^{m\cdot n\cdot p}$  
  

•  $a^{m\cdot p}\ b^{n\cdot p}$  

•  $a^mb^n$  
  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

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

• $16x^3y^2$

• $4x^6y^4$

• $16x^6y^4$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify the following:
 $\left(x^2y^4m^3\right)^8$  

•  $x^{10}y^{12}m^{11}$  

•  $x^6y^{-4}m^{-5}$  

•  $x^{16}y^{32}m^{24}$  

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

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

•  $\frac{a^m+a^p}{b^n+b^p}$  

•  $a^{m\cdot p}\ b^{n\cdot p}$  
  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

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

• It's like "distributing" the power to each part of the top and bottom

• We subtract m and n, then multiply by p

• We exponent-ize everything

Tags

CCSS.HSA.SSE.B.3

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

•  $\frac{x^8}{y^{12}}$  

•  $\frac{x^6}{y^7}$  

•  $x^8y^{12}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify the following:
 $\left(\frac{x^2y}{z^3}\right)^5$ 

•  $\frac{x^{10}y^5}{z^{15}}$ 

•  $\frac{x^{10}y}{z^{15}}$ 

•  $\frac{x^{10}y}{z^3}$ 

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2