Question

(5^2)^n x 5^4 = 5^10 find n

Answer 1

Answer:

${ ({5}^{2} )}^{n} \times {5}^{4} = {5}^{10} \\ {5}^{ 2n } \times {5}^{4} = {5}^{10} \\ {(5)}^{2n + 4} = {(5)}^{10}$

Now, as the bases are same, equating the powers.

$2n + 4 = 10 \\ 2n = 10 - 4 \\ 2n = 6 \\ n = \frac{6}{2 } \\ n = 3$

Hence, the value of n is 3.