Question

(6/5)^x multiply(5/6)^-2x=125/216

Answer 1

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Answer 2

Answer:

$\sf\huge \implies: \frac{36}{25}$

Step-by-step explanation:

$\sf\huge {( \frac{6}{5} })^{x} \times ({ \frac{5}{6} })^{ - 2x} \\ \\ \sf\ \implies: \frac{ {6}^{x} }{ {5}^{x} } \times \frac{ {5}^{ - 2x} }{ {6}^{ - 2x} } \\ \\ \sf\ \implies: \frac{ {6}^{x} }{ {5}^{x} } \times \frac{ {5}^{ - 2} \times {5}^{x} }{ {6}^{ - 2} \times {6}^{x} } \\ \\ \sf\ \implies: \frac{ {6}^{x} }{ {5}^{x} } \times \frac{ \frac{1}{ {5}^{2} } \times {5}^{x} }{ \frac{1}{ {6}^{2} } \times {6}^{x} } \\ \\ \sf\ \implies: \frac{ {6}^{x} }{ {5}^{x} } \times \frac{ \frac{ {5}^{x} }{ {5}^{2} } }{ \frac{ {6}^{x} }{ {6}^{2} } } \\ \\ \sf\ \implies: \frac{ \cancel{6}^{x} }{ \cancel{5}^{x} } \times \frac{\cancel {5}^{x} }{ {5}^{2} } \times \frac{ {6}^{2} }{ \cancel{6}^{x} } \\ \\ \sf\huge \implies: \frac{36}{25}$