Question

Simplify-[81/16]^-3/4 multiplied by [25/9]^-3/2 divided by[5/2]^-3

Answer 1

Heya there !!!
Here is the answer you were looking for:
${( \frac{81}{16} )}^{ - \frac{3}{4} } \times {( \frac{25}{9} )}^{ - \frac{3}{2} } \div {( \frac{5}{2} )}^{ - 3}$

We know that,

${( \frac{a}{b} )}^{ - m} = {( \frac{b}{a} )}^{m}$

$= {( \frac{16}{81} )}^{ \frac{3}{4} } \times {( \frac{9}{25} )}^{ \frac{3}{2} } \div {( \frac{2}{5} )}^{3} \\ \\ = {( \frac{16}{81} )}^{ \frac{3}{4} } \times {( \frac{9}{25} )}^{ \frac{3}{2} } \times {( \frac{5}{2} )}^{3} \\ \\ = {( \frac{ {2}^{4} }{ {3}^{4} } )}^{ \frac{3}{4} } \times {( \frac{ {3}^{2} }{ {5}^{2} } )}^{ \frac{3}{2} } \times {( \frac{5}{2} )}^{3} \\ \\ = {( \frac{2}{3} )}^{4 \times \frac{3}{4} } \times {( \frac{3}{5} )}^{2 \times \frac{3}{2} } \times {( \frac{5}{2} )}^{3} \\ \\ = {( \frac{2}{3} )}^{3} \times {( \frac{3}{5} )}^{3} \times {( \frac{5}{2} )}^{3} \\ \\ = \frac{ {2}^{3} }{ {3}^{3} } \times \frac{ {3}^{3} }{ {5}^{3} } \times \frac{ {5}^{3} }{ {2}^{3} } \\ \\ = \frac{1}{1} \\ \\ = 1$

Hope you understood !!!

If you have any doubt regarding to my answer, then feel free to ask in the comment section ^_^

@Mahak24

Thanks...
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