Question

Вычислите значение выражения

Answer 1

$\frac{ {6}^{4} \times {9}^{2} }{ {12}^{5} } \div {( \frac{3}{20} )}^{3} = \frac{ {6}^{4} \times {9}^{2} }{ {12}^{5} } \times {( \frac{20}{3} )}^{3}$

$\frac{ {6}^{4} \times {9}^{2} }{ {12}^{5} } = \frac{ {(2 \times 3)}^{4} \times {(3 \times 3)}^{2} }{ {(2 \times 2 \times 3)}^{5} } = \frac{ {2}^{4} \times {3}^{4} \times {3}^{2} \times {3}^{2} }{ {2}^{5} \times {2}^{5} \times {3}^{5} } = \frac{3 \times {3}^{2} }{2 \times {2}^{5} } = \frac{ {3}^{3} }{ {2}^{6} }$

${( \frac{20}{3} )}^{3} = \frac{ {20}^{3} }{ {3}^{3} }$

=>

$\frac{ {3}^{3} }{ {2}^{6} } \times \frac{ {20}^{3} }{ {3}^{3} } = \frac{ {3}^{3} \times {2}^{3} \times {2}^{3} \times {5}^{3} }{ {2}^{6} \times {3}^{3} } = {5}^{3} = 125$