Write the following in exponential form assuming denominators not equal to zero:
$x^{5} \div x^{3}$

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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, $x^{5} \div x^{3}$ $= x^{5 - 3}$ where $a = x, m = 5, n = 3$
$= x^{2}$ .
Therefore, $x^{5} \div x^{3}$ $= x^{2}$ .

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