Question

evaluate it

please write correct answer with Steps.

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Answer 1

${( \frac{5}{8}) }^{ - 7} \times {( \frac{8}{5}) }^{ - 4} \\ \\ = \frac{1}{ {( \frac{5}{8}) }^{7} } \times {( \frac{8}{5}) }^{ - 4} \\ \\ because \: if \: \: \: \: \: \: {x}^{ - 1} = \frac{1}{x} \\ \\ = {( \frac{8}{5} )}^{7} \times {( \frac{8}{5} )}^{ - 4} \\ \\ because \: \: \: \: \: \frac{1}{( \frac{a}{b} )} = \frac{b}{a} \\ \\ = {( \frac{8}{5} )}^{7 - 4} \\ \\ because \: \: \: \: \: \: \: {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \\ = {( \frac{8}{5} )}^{3} \\ \\ = \frac{512}{125}$

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