Question
Find the value of m for which $5^m$ $\div$ $5^{-3}= 5^5$
✓
Answer
$5^m$ $\div$ $5^{-3}= 5^5$
$\therefore \frac{{{5^m}}}{{{5^{ - 3}}}} = {5^5}$
$\therefore$ $ 5^{m-(-3)}= 5^5 $
$\therefore$ $ 5^{m+3}= 5^5 $
$\therefore$ $m + 3 = 5$ [When the bases are same , powers are equal]
$\therefore$ $m = 5 – 3$
$\therefore$ $m = 2$
$\therefore \frac{{{5^m}}}{{{5^{ - 3}}}} = {5^5}$
$\therefore$ $ 5^{m-(-3)}= 5^5 $
$\therefore$ $ 5^{m+3}= 5^5 $
$\therefore$ $m + 3 = 5$ [When the bases are same , powers are equal]
$\therefore$ $m = 5 – 3$
$\therefore$ $m = 2$
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