Question
Simplify the following: $\frac{5^{\text{n}+3}-6\times5^{\text{n+1}}}{9\times5^{\text{x}}-2^2\times5^{\text{n}}}$
✓
Answer
$\frac{(5^{\text{n}+3})-(6\times5^{\text{n}+1})}{(9\times5^{\text{n}})-(2^2\times5^\text{n})}$
$=\frac{(5^{\text{n}+3})-(6\times5^{\text{n}+1})}{(9\times5^{\text{n}})-(2^2\times5^{\text{n}})}$
$=\frac{(5^\text{n}\times5^3)-(6\times5^\text{n}\times5)}{(9\times5^\text{n})-(2^2\times\text{5}^\text{n})}$
$=\frac{5^\text{n}(125-30)}{5^{\text{n}(9-4)}}$
$=\frac{95}{5}=19$
$=\frac{(5^{\text{n}+3})-(6\times5^{\text{n}+1})}{(9\times5^{\text{n}})-(2^2\times5^{\text{n}})}$
$=\frac{(5^\text{n}\times5^3)-(6\times5^\text{n}\times5)}{(9\times5^\text{n})-(2^2\times\text{5}^\text{n})}$
$=\frac{5^\text{n}(125-30)}{5^{\text{n}(9-4)}}$
$=\frac{95}{5}=19$
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