Question

slove using exponents (81/16)^-3/4 [(25/9)^-3/2 ÷(5/2)^-3]​

Answer 1

Question :-

Solve -

$\implies\sf \Big( \dfrac{81}{16} \Big)^{ \frac{ - 3}{4} } \times \Big[\Big(\dfrac{25}{9}\Big)^{\frac{-3}{2}} \div \Big(\dfrac{5}{2}\Big)^{-3}$

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Answer :-

$\implies\sf \Big( \dfrac{81}{16} \Big)^{ \frac{ - 3}{4} } \times \dfrac{\Big(\dfrac{25}{9}\Big)^{\frac{-3}{2}}}{\Big(\dfrac{5}{2}\Big)^{-3}}$

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• $\sf a^{-n} = \dfrac{1}{n}$

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$\implies\sf \Big( \dfrac{81}{16} \Big)^{ \frac{ - 3}{4} } \times \Big(\dfrac{25}{9}\Big)^{\frac{-3}{2}} \times \Big(\dfrac{5}{2}\Big)^{3}$

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$\implies\sf \Big( \dfrac{81}{16} \Big)^{ \frac{ - 3}{4} } \times \dfrac{\Big(\dfrac{5}{2}\Big)^{3}}{\Big(\dfrac{25}{9}\Big)^{\frac{3}{2}}}$

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$\implies\sf \dfrac{1}{\Big( \dfrac{81}{16} \Big)^{ \frac{3}{4} }} \times \dfrac{\Big(\dfrac{5}{2}\Big)^{3}}{\Big(\dfrac{25}{9}\Big)^{\frac{3}{2}}}$

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$\implies\sf \dfrac{1}{\Big( \dfrac{3^4}{2^4} \Big)^{ \frac{3}{4}}} \times \dfrac{\dfrac{5^3}{2^3}}{\Big(\dfrac{5^2}{3^2}\Big)^{\frac{3}{2}}}$

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$\implies\sf \Big(\dfrac{2^4}{3^4}\Big)^\frac{3}{4} \times \dfrac{\dfrac{5^3}{2^3}}{\dfrac{5^{2\times \frac{3}{2}}}{3^{2\times \frac{3}{2}}}}$

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$\implies\sf \dfrac{2^{4 \times \frac{3}{4}}}{3^{4 \times \frac{3}{4}}} \times \dfrac{\dfrac{5^3}{2^3}}{\dfrac{5^3}{2^3}}$

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$\implies\sf \dfrac{2^3}{3^3} \times \dfrac{5^3 \times 3^3}{5^3 \times 2^3}$

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$\implies\boxed{\sf 1}$