Question

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Answer 1

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