Write the following in exponential form assuming denominators not equal to zero:
$y^{5} \div y^{2}$

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

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