# How do you simplify 4^6/4^8?

Jan 22, 2016

$\frac{1}{16}$

#### Explanation:

using : ${a}^{m} = \frac{1}{a} ^ - m \Leftrightarrow {a}^{-} m = \frac{1}{a} ^ m$

then : ${4}^{6} / {4}^{8} = \frac{1}{4} ^ \left(8 - 6\right) = \frac{1}{4} ^ 2 = \frac{1}{16}$

Feb 8, 2016

$= \frac{1}{16}$

#### Explanation:

${4}^{6} / {4}^{8}$

color(green)(4^6=4*4*4*4*4*4

color(blue)(4^8=4*4*4*4*4*4*4*4

So,

${4}^{6} / {4}^{8} =$

$\rightarrow \frac{\textcolor{g r e e n}{4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4}}{\textcolor{b l u e}{4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4}}$

$\rightarrow \frac{\textcolor{g r e e n}{\cancel{4} \cdot \cancel{4} \cdot \cancel{4} \cdot \cancel{4} \cdot \cancel{4} \cdot \cancel{4}}}{\textcolor{b l u e}{\cancel{4} \cdot \cancel{4} \cdot \cancel{4} \cdot \cancel{4} \cdot \cancel{4} \cdot \cancel{4} \cdot 4 \cdot 4}} =$

$\rightarrow \frac{\textcolor{g r e e n}{1}}{\textcolor{b l u e}{4 \cdot 4}} = \frac{\textcolor{g r e e n}{1}}{\textcolor{b l u e}{16}}$