Question

$\frac{5^{10+n}\times {25}^{3n-4}}{5^{7n}}$ = ___

Answer 1

Given:

$\frac{5^{10+n}\times {25}^{3n-4}}{5^{7n}}$

$\Rightarrow$ $\frac{5^{10+n}\times (5^2{)}^{3n-4}}{5^{7n}}$

$\because (a^m{)}^n=(a{)}^{m\times n}$

$\Rightarrow$ $\frac{5^{10+n}\times 5^{6n-8}}{5^{7n}}$

$\because a^m\times a^n=a^{(m+n)}$ and $\frac{a^m}{a^n}=a^{(m-n)}$

$\Rightarrow$ $5^{10+n+6n-8-7n}$

$\Rightarrow$ $5^2$ = 25