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Find the value of $x$ for which $5^{2x} \div 5^{-3}= 5^{5}$.
Given:
$5^{2x} \div5^{-3}= 5^{5}$.
To do:
We have to find the value of \( x \).
Solution:
We know that,
$a^m \times a^n=a^{m+n}$
$5^{2 x}\div 5^{-3}=5^{5}$
$5^{2 x} \times 5^{3}=5^{5}$
$5^{2x+3}=5^5$
Comparing both sides, we get,
$2x+3=5$
$2x=5-3$
$2x=2$
$x=\frac{2}{2}$
$x=1$
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