# How do you simplify 15^4/15^6?

May 25, 2016

$\frac{1}{225}$

#### Explanation:

Consider the example of ${a}^{2}$, this is ${a}^{1} \times {a}^{1} = {a}^{2} = {a}^{1 + 1}$

So ${a}^{5}$, if so chosen, could be written as ${a}^{2 + 3} = {a}^{2} \times {a}^{3}$

$\textcolor{b l u e}{\text{Back to your question}}$

$\textcolor{b r o w n}{\text{Method 1}}$

Write ${15}^{4} \text{ as } {15}^{4} \times 1$

Write ${15}^{6} \text{ as } {15}^{4 + 2} = {15}^{4} \times {15}^{2}$

So ${15}^{4} / {15}^{6} = \frac{{15}^{4} \times 1}{{15}^{4} \times {15}^{2}}$

This is the same as ${15}^{4} / {15}^{4} \times \frac{1}{15} ^ 2$

But ${15}^{4} / {15}^{4} = 1$ giving

$\textcolor{b r o w n}{{15}^{4} / {15}^{6} = \frac{1}{15} ^ 2 = \frac{1}{225}}$
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$\textcolor{b r o w n}{\text{Method 2}}$

Consider the example:$\frac{1}{a} ^ 2 = {a}^{- 2}$

Write ${15}^{4} / {15}^{6} \text{ as } {15}^{4} \times {15}^{- 6}$

$\textcolor{b r o w n}{= {15}^{4 - 6} = {15}^{- 2} = \frac{1}{15} ^ 2 = \frac{1}{225}}$