Question

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Answer 1

Step-by-step explanation:

$( { \frac{64}{125} })^{ - \frac{2}{3} } + \frac{1}{( \frac{256}{625})^{ \frac{1}{4} } } + \frac{ \sqrt{25} }{ \sqrt[3]{64} } \\ = \sqrt[3]{ { (\frac{64}{125} )}^{ - 2} } + \frac{1}{ \sqrt[4]{ \frac{256}{625} } } + \frac{ \sqrt{25} }{ \sqrt[3]{64} } \\ = \sqrt[3]{ ({ \frac{125}{64}) }^{2} } + \sqrt[4]{ \frac{625}{256} } + \frac{ \sqrt{25} }{ \sqrt[3]{64} } \\ = \sqrt[3]{ \frac{125 \times 125}{64 \times 64} } + \sqrt[4]{ \frac{5 \times 5 \times 5 \times 5}{4 \times 4 \times 4 \times 4 } } + \frac{ \sqrt{5 \times 5} }{ \sqrt[3]{4 \times 4 \times 4} } \\ = \sqrt[3]{ \frac{25 \times 25 \times2 5}{16 \times 16 \times 16} } + \frac{5}{4} + \frac{5}{4} \\ = \frac{25}{16} + \frac{10}{4} \\ = \frac{25 + 40}{16} = \frac{65}{16}$