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Find the value of $ n $ when $ 5^{2 n} \times 5^{3}=5^{9} $.
Given :
The given expression is $5^{2n} \times 5^3 = 5^9$
To do :
We have to find the value of n.
Solution :
We know that,
$a^m \times a^n=a^{m+n}$
Therefore,
$5^{2n} \times 5^3 = 5^9$
$5^{2n+3} = 5^9$
Comparing the powers on both sides,
$2n+3 = 9$
$2n = 9-3$
$2n = 6$
$n=\frac{6}{2}$
$n=3$
The value of n is $3$.
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