Write the following in exponential form assuming denominators not equal to zero:
${(\frac{m}{n})}^{6} \div {(\frac{m}{n})}^{4}$

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Solution

For any non-zero integer $a$ , where $m$ and $n$ are whole numbers and $m > n$ .
$a^{m} \div a^{n} = \frac{a^{m}}{a^{n}} = a^{m - n}$
So, ${(\frac{m}{n})}^{6} \div {(\frac{m}{n})}^{4}$ $= {(\frac{m}{n})}^{6 - 4}$ where $a = \frac{m}{n}, m = 6, n = 4$
$= {(\frac{m}{n})}^{2}$ .
Therefore, ${(\frac{m}{n})}^{6} \div {(\frac{m}{n})}^{4}$ $= {(\frac{m}{n})}^{2}$ .

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