Question

(iii) (32)-2/5÷
(125)-2/3​

Answer 1

Answer:

calculator;31.3301333333

me:32.6634666667

Answer 2

$\red{ \sf \: (32) ^{ - \frac{2}{5} } \div (125) ^{ - \frac{2}{3} } }$

$\huge \green{solution : }$

$\implies \tt \bigg [\frac{(32) ^{ - \frac{2}{3} } }{ {(125)}^{ - \frac{2}{3} } } \bigg]$

$\implies \sf \: \frac{ {(125)}^{ \frac{2}{3} } }{ {(32)}^{ \frac{2}{3} } }$

$\implies \sf \: \frac{(5 \times 5 \times 5) ^{ \frac{2}{3} } }{ {(2 \times 2 \times 2 \times 2 \times 2) }^{ \frac{2}{5} } }$

$\implies \sf \: \frac{ {(5}^{3} {)}^{ \frac{2}{3} } }{( {2}^{5} {)}^{ \frac{2}{5} } }$

$\implies \sf \: \frac{(5) ^{ \cancel{3} \times \frac{2}{ \cancel{3}} } }{(2) ^{ \cancel{5} \times \frac{2}{{ \cancel{5}}} } }$

$\implies \sf \: \frac{ {5}^{2} }{ {2}^{2} }$

$\implies \sf \: \frac{ \cancel{25}}{ \cancel{4} ^{} }$

$\boxed{ \implies \sf \: 6 \frac{1}{4} }$