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

A. $\frac{1}{3}$

B. $\frac{1}{48}$

C. 1

D. 48

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}

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