6.2 Use multiplication properties of exponents

Solution

ⓐ
$\begin{array}{cccc}& & & 4^3\hfill \\ \text{Multiply three factors of 4.}\hfill & & & 4·4·4\hfill \\ \text{Simplify.}\hfill & & & 64\hfill \end{array}$

ⓑ
$\begin{array}{cccc}& & & 7^1\hfill \\ \text{Multiply one factor of 7.}\hfill & & & 7\hfill \end{array}$

ⓒ
$\begin{array}{cccc}& & & {\left(\frac{5}{6}\right)}^2\hfill \\ \text{Multiply two factors.}\hfill & & & \left(\frac{5}{6}\right)\left(\frac{5}{6}\right)\hfill \\ \text{Simplify.}\hfill & & & \frac{25}{36}\hfill \end{array}$

ⓓ
$\begin{array}{cccc}& & & {\left(0.63\right)}^2\hfill \\ \text{Multiply two factors.}\hfill & & & \left(0.63\right)\left(0.63\right)\hfill \\ \text{Simplify.}\hfill & & & 0.3969\hfill \end{array}$

Solution

1. ⓐ
   $\begin{array}{cccc}& & & {\left(\mathrm{-5}\right)}^4\hfill \\ \text{Multiply four factors of}\mathrm{-5}.\hfill & & & \left(\mathrm{-5}\right)\left(\mathrm{-5}\right)\left(\mathrm{-5}\right)\left(\mathrm{-5}\right)\hfill \\ \text{Simplify.}\hfill & & & 625\hfill \end{array}$
   
   
2. ⓑ
   $\begin{array}{cccc}& & & \text{−}{5}^4\hfill \\ \text{Multiply four factors of 5.}\hfill & & & \text{−}\left(5·5·5·5\right)\hfill \\ \text{Simplify.}\hfill & & & \mathrm{-625}\hfill \end{array}$

Solution

Use the product property, a m · a n = a m+n .
Simplify.

Solution

1. ⓐ
   

   Use the product property, a m · a n = a m+n .
   Simplify.

2. ⓑ
   

   Use the product property, a m · a n = a m+n .
   Simplify.

Solution

1. ⓐ
   

   Rewrite, a = a 1 .
   Use the product property, a m · a n = a m+n .
   Simplify.

2. ⓑ
   

   Notice, the bases are the same, so add the exponents.
   Simplify.