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 $3$.