# How do you evaluate 6^5/6^2?

Apr 2, 2018

${6}^{3}$ = 216

#### Explanation:

Using the index laws
$\frac{{a}^{m}}{{a}^{n}}$ = ${a}^{m - n}$

${6}^{5} / {6}^{2}$ = ${6}^{5 - 2}$ = ${6}^{3}$ = 216

Apr 2, 2018

${6}^{3}$ = 216

#### Explanation:

When dividing two numbers with exponents, which have the same base, you can just subtract the exponents from eachother like this:
$\frac{{a}^{b}}{{a}^{c}} = {a}^{b - c}$
and similarly (eventhough its not relevant to this problem,)
$\left({a}^{b}\right) \cdot \left({a}^{c}\right) = {a}^{b + c}$
therefor:
$\frac{{6}^{5}}{{6}^{2}} = {6}^{5 - 2} = {6}^{3} = 6 \cdot 6 \cdot 6 = 216$