Question

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Answer 1

$\frac{{18}^{2} \times 10^{2} }{ {15}^{3} \times {12}^{5} } = \\ = \frac{(9 \times 2) ^{2} \times {(2 \times 5)}^{2} }{ {(3 \times 5)}^{3} \times {(4 \times 3)}^{5} } = \\ = \frac{( {3}^{2} \times 2) ^{2} \times {(2 \times 5)}^{2} }{ {(3 \times 5)}^{3} \times {( {2}^{2} \times 3)}^{5} } = \\ = \frac{ {( {3}^{2} )}^{2} \times {2}^{2} \times {2}^{2} \times {5}^{2} }{ {3}^{3} \times {5}^{3} \times { ({2}^{2}) }^{5} \times {3}^{5} } = \\ = \frac{ {3}^{4} \times {2}^{4} \times {5}^{2} }{ {3}^{8} \times {2}^{10} \times {5}^{3} } = \\ = \frac{1}{ {3}^{4} \times {2}^{6} \times 5 } = \\ = \frac{1}{81 \times 64 \times 5} = \\ = \frac{1}{25920}$