6.2 Use multiplication properties of exponents  (Page 2/3)

Solution

Add the exponents, since bases are the same.
Simplify.

Solution

ⓐ

Use the power property, ( a m ) n = a m·n .
Simplify.

Use the power property.
Simplify.

Solution

1. ⓐ
   

   Use Power of a Product Property, ( ab ) m = a m b m .
   Simplify.

2. ⓑ
   

   Use Power of a Product Property, ( ab ) m = a m b m .
   Simplify.

Solution

1. ⓐ
   $\begin{array}{cccc}& & & {(y^3)}^6{(y^5)}^4\hfill \\ \text{Use the Power Property.}\hfill & & & y^{15}·y^{20}\hfill \\ \text{Add the exponents.}\hfill & & & y^{35}\hfill \end{array}$
   
   
2. ⓑ
   $\begin{array}{cccc}& & & {\left(\mathrm{-6}{x}^4{y}^5\right)}^2\hfill \\ \text{Use the Product to a Power Property.}\hfill & & & {(\mathrm{-6})}^2{(x^4)}^2{(y^5)}^2\hfill \\ \text{Use the Power Property.}\hfill & & & {(\mathrm{-6})}^2(x^8)(y^{10})\hfill \\ \text{Simplify.}\hfill & & & 36x^8{y}^{10}\hfill \end{array}$

Solution

1. ⓐ
   $\begin{array}{cccc}& & & {(5m)}^2(3m^3)\hfill \\ \text{Raise}5m\text{to the second power.}\hfill & & & 5^2{m}^2·3m^3\hfill \\ \text{Simplify.}\hfill & & & 25m^2·3m^3\hfill \\ \text{Use the Commutative Property.}\hfill & & & 25·3·m^2·m^3\hfill \\ \text{Multiply the constants and add the exponents.}\hfill & & & 75m^5\hfill \end{array}$
   
   
2. ⓑ
   $\begin{array}{cccc}& & & {(3x^{2}y)}^4{(2x{y}^2)}^3\hfill \\ \text{Use the Product to a Power Property.}\hfill & & & (3^4{x}^8{y}^4)(2^3{x}^3{y}^6)\hfill \\ \text{Simplify.}\hfill & & & (81x^8{y}^4)(8x^3{y}^6)\hfill \\ \text{Use the Commutative Property.}\hfill & & & 81·8·x^8·x^3·y^4·y^6\hfill \\ \text{Multiply the constants and add the exponents.}\hfill & & & 648x^{11}{y}^{10}\hfill \end{array}$