Question

Simplify the following.

$\frac{2 \times {3}^{4} \times {2}^{5} }{ {3}^{2} \times {4}^{5} }$
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Answer 1

$\frac{2 \times {3}^{4} \times {2}^{5} }{ {3}^{2} \times {4}^{5} } \\ \\ \to \frac{2 \times {3}^{4} \times {2}^{5} }{ {3}^{2} \times {(2 \times 2)}^{5} } \\ \\ \to \frac{ {2}^{1} \times {3}^{4} \times {2}^{5} }{ {3}^{2} \times {2}^{5} \times {2}^{5} } \\ \\ \to \frac{ {2}^{(1 + 5)} \times {3}^{4} }{ {3}^{2} \times {2}^{(5 + 5)} } \\ \\ \to \frac{ {2}^{6} \times {3}^{4} }{ {3}^{2} \times {2}^{10} } \\ \\ \to \frac{ {3}^{4 - 2} }{ {2}^{10 - 6} } \\ \\ \to \frac{ {3}^{2} }{ {2}^{4} } \\ \\ \to \frac{ 3 \times 3 }{ 2 \times 2 \times 2 \times 2 } \\ \\ \to \frac{ 9 }{ 16 }$

Answer is 9 upon 16.