${(48)}^{- \frac{2}{7}} \times {(16)}^{- \frac{5}{7}} \times {(3)}^{- \frac{5}{7}} = ?$ ${\left( {48} \right)^{ - \frac{2}{7}}} \times {\left( {16} \right)^{ - \frac{5}{7}}} \times {\left( 3 \right)^{ - \frac{5}{7}}} = ?$

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} {(48)}^{- \frac{2}{7}} \times {(16)}^{- \frac{5}{7}} \times {(3)}^{- \frac{5}{7}} \\ = {(16 \times 3)}^{- \frac{2}{7}} \times {(16)}^{- \frac{5}{7}} \times {(3)}^{- \frac{5}{7}} \\ = {(16)}^{- \frac{2}{7}} \times {(3)}^{- \frac{2}{7}} \times {(16)}^{- \frac{5}{7}} \times {(3)}^{- \frac{5}{7}} \\ = {(16)}^{(- \frac{2}{7} - \frac{5}{7})} \times {(3)}^{(- \frac{2}{7} - \frac{5}{7})} \\ = {(16)}^{(- \frac{7}{7})} \times {(3)}^{(- \frac{7}{7})} \\ = {(16)}^{- 1} \times {(3)}^{- 1} \\ = \frac{1}{16} \times \frac{1}{3} \\ = \frac{1}{48} \end{aligned}

$\eqalign{ & {\left( {48} \right)^{ - \frac{2}{7}}} \times {\left( {16} \right)^{ - \frac{5}{7}}} \times {\left( 3 \right)^{ - \frac{5}{7}}} \cr & = {\left( {16 \times 3} \right)^{ - \frac{2}{7}}} \times {\left( {16} \right)^{ - \frac{5}{7}}} \times {\left( 3 \right)^{ - \frac{5}{7}}} \cr & = {\left( {16} \right)^{ - \frac{2}{7}}} \times {\left( 3 \right)^{ - \frac{2}{7}}} \times {\left( {16} \right)^{ - \frac{5}{7}}} \times {\left( 3 \right)^{ - \frac{5}{7}}} \cr & = {\left( {16} \right)^{\left( { - \frac{2}{7} - \frac{5}{7}} \right)}} \times {\left( 3 \right)^{\left( { - \frac{2}{7} - \frac{5}{7}} \right)}} \cr & = {\left( {16} \right)^{\left( { - \frac{7}{7}} \right)}} \times {\left( 3 \right)^{\left( { - \frac{7}{7}} \right)}} \cr & = {\left( {16} \right)^{ - 1}} \times {\left( 3 \right)^{ - 1}} \cr & = \frac{1}{{16}} \times \frac{1}{3} \cr & = \frac{1}{{48}} \cr}$