Question

$(12 \div 25) {}^{2} \times (15 \div 2) {}^{3} \div (9 \div 2) {}^{2}$

Answer 1

Hey friend,
Here is the answer you were looking for:
${( \frac{12}{25} )}^{2} \times {( \frac{15}{2} )}^{3} \div {( \frac{9}{2} )}^{2} \\ \\ = {( \frac{12}{ 25 } )}^{2} \times {( \frac{15}{2} )}^{3} \times {( \frac{2}{9} )}^{2} \\ \\ = (\frac{ {12}^{2} }{ {25}^{2} } ) \times (\frac{ {15}^{3} }{ {2}^{3} } ) + ( \frac{ {2}^{2} }{ {9}^{2} } ) \\ \\ = \frac{ {12}^{2} \times {15}^{3} \times {2}^{2} }{ {25}^{2} \times {2}^{3} \times {9}^{2} } \\ \\ = \frac{ {3}^{2} \times {2}^{2} \times {2}^{2} \times {5}^{3} \times {3}^{3} \times {2}^{2} }{ {5}^{2} \times {5}^{2} \times {2}^{3} \times {3}^{2} \times {3}^{2} } \\ \\ using \: the \: identity \\ {a}^{m} \times {a}^{n} = {a}^{m + n} \\ \\ = \frac{ {3}^{2 + 3} \times {2}^{2 + 2 + 2} \times {5}^{3} }{ {5}^{2 + 2 } \times {2}^{3} \times {3}^{2 + 2} } \\ \\ = \frac{ {3}^{5} \times {2}^{6} \times {5}^{3} }{ {5}^{4} \times {2}^{3} \times {3}^{4} } \\ \\ using \: the \: identity \\ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ \\ = {3}^{5 - 4} \times {2}^{6 - 3} \times {5}^{3 - 4} \\ \\ = {3}^{1} \times {2}^{3} \times {5}^{ - 1} \\ \\ = 3 \times 8 \times \frac{1}{5} \\ \\ = \frac{24}{5}$

Hope this helps!!!!

@Mahak24

Thanks...
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