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Simplify: \( \frac{2^{2} \times 3^{4} \times 2^{5}}{2^{4} \times 9} \)
Given:
\( \frac{2^{2} \times 3^{4} \times 2^{5}}{2^{4} \times 9} \).
To do:
We have to simplify \( \frac{2^{2} \times 3^{4} \times 2^{5}}{2^{4} \times 9} \).
Solution:
We know that,
$a^m \times a^n= a^{m+n}$
$\frac{a^m}{a^n}=a^{m-n}$
$\frac{2^{2} \times 3^{4} \times 2^{5}}{2^{4} \times 9} =\frac{2^{2} \times 3^{4} \times 2^{5}}{2^{4} \times 3^2}$
$=2^{2+5-4}\times3^{4-2}$
$=2^3\times3^2$
$=8\times9$
$=72$
Therefore,
$\frac{2^{2} \times 3^{4} \times 2^{5}}{2^{4} \times 9} =72$.
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