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

Given:

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

To do:

We have to simplify the given expression.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$  

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

$=\frac{125-30}{9-4}$

$=\frac{95}{5}$

$=19$

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

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Updated on: 10-Oct-2022

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