Question

Simplify the following:

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

Answer 1

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

$=\frac{5^n\times 5^3-6\times 5^n\times 5}{9\times 5^n-4\times 5^n}$

$[\because a^m\times a^n=a^{m+n}]$

$=\frac{5^n(5^3-6\times 5)}{5^n(9-4)}$

$=\frac{125-30}{5}$

$=\frac{95}{5}$

$=19$

$\therefore \frac{5^{n+3}-6\times 5^{n+1}}{9\times 5^n-2^2\times 5^n}=19$