Simplify: 2 3^ 4 2^ 5 9 4^ 2 - Vidyadip

Question

Simplify: $\frac{2 \times 3^{4} \times 2^{5}}{9 \times 4^{2}}$

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Answer

Here,
$\frac{2 \times 3^{4} \times 2^{5}}{9 \times 4^{2}}=\frac{2 \times 3^{4} \times 2^{5}}{3^{2} \times\left(2^{2}\right)^{2}}=\frac{2 \times 2^{5} \times 3^{4}}{3^{2} \times 2^{2 \times 2}}$$=\frac{2^{1+5} \times 3^{4}}{2^{4} \times 3^{2}}=\frac{2^{6} \times 3^{4}}{2^{4} \times 3^{2}}$
$=2^{6-4} \times 3^{4-2}$
$=2^2 \times 3^2$
= $4 \times 9 = 36$

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