Powers of Products and Quotients

 $ab^{m\cdot n\cdot p}$  

 $a^{m\cdot p}\ b^{n\cdot p}$  

 $a^mb^n$  

It's like "distributing" the power

We add the powers together

We divide the powers

 $r^7s^9$  

 $r^{21}s^9$  

 $r^{21}s^3$  

 $a^5b^5c^{25}$ 

 $a^5b^5c^5$ 

 $abc^{25}$ 

$16x^3y^2$

$4x^6y^4$

$16x^6y^4$

 $x^{10}y^{12}m^{11}$  

 $x^6y^{-4}m^{-5}$  

 $x^{16}y^{32}m^{24}$  

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

 $\frac{a^m+a^p}{b^n+b^p}$  

 $a^{m\cdot p}\ b^{n\cdot p}$  

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

 $\frac{x^8}{y^{12}}$  

 $\frac{x^6}{y^7}$  

 $x^8y^{12}$  

 $\frac{x^{10}y^5}{z^{15}}$ 

 $\frac{x^{10}y}{z^{15}}$ 

 $\frac{x^{10}y}{z^3}$