Question

(64/125)^-2/3+1/(256/625)^1/4+(√25/3√64)

Answer 1

## here is your answer ##

$( \frac{64}{125} {)}^{ \frac{ - 2}{3} } + \frac{1}{( \frac{256}{625} {)}^{ \frac{1}{4} } } + ( \frac{ \sqrt{25} }{3 \sqrt{64} } ) \\ \\ = ( \frac{125}{64} {)}^{ \frac{2}{3} } + ( \frac{625}{256} {)}^{ \frac{1}{4} } + \frac{5}{3 \times 8} \\ \\ = ( \frac{5}{4} {)}^{3 \times \frac{2}{3} } + ( \frac{5}{4} {)}^{4 \times \frac{1}{4} } + \frac{5}{24} \\ \\ = ( \frac{5}{4} {)}^{2} \: + ( \frac{5}{4} {)}^{1} + \frac{5}{24} \\ \\ = common \: factor \: = \: \frac{5}{4} \\ \\ = \frac{5}{4} \: \: ( \: \: \frac{5}{4} + 1 + \frac{5}{6} ) \\ \\ = \frac{5}{4} \: ( \: \frac{5 \times 3 + 1 \times 12 + 5 \times 2}{12} ) \\ \\ = \frac{5}{4} \: ( \: \frac{15 + 12 + 10}{12} ) \\ \\ = \: \frac{5}{4} \times \frac{37}{12} \\ \\ = \frac{185}{48}$

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