Question

Simplify:
$\frac{5^{n+3}-6\times 5^{n+1}}{9\times 5^n-5^n\times 2^2}$

Answer 1

Step: Simplifying the given expression
Given: $\frac{5^{n+3}-6\times 5^{n+1}}{9\times 5^n-5^n\times 2^2}$
it can be simplified as:
$\frac{5^n\times 5^3-6\times 5^n\times 5^1}{9\times 5^n-5^n\times 2^2}$
$[\because a^{m+n}=a^m\times a^n]$
$=\frac{5^n(5^3-6\times 5)}{5^n\times (9-2^2)}$
$=\frac{125-30}{9-4}$
$=\frac{94}{5}=19$
Hence, the simplified value is $19$.