Evaluate the following :(81/16)^(-3/4) × {[25/9]^(-3/2) ÷ [5/2]^-3}

Given, Simplifying the expression : Hence, .

Mathematics

Evaluate the following :
$\Big(\dfrac{81}{16}\Big)^{-\dfrac{3}{4}} \times \Big[\Big(\dfrac{25}{9}\Big)^{-\dfrac{3}{2}} ÷ {\Big(\dfrac{5}{2}\Big)^{-3}}\Big]$

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Answer

Given,

$\Big(\dfrac{81}{16}\Big)^{-\dfrac{3}{4}} \times \Big[\Big(\dfrac{25}{9}\Big)^{-\dfrac{3}{2}} ÷ {\Big(\dfrac{5}{2}\Big)^{-3}}\Big]$

Simplifying the expression :

$\Rightarrow \Big(\dfrac{81}{16}\Big)^{-\dfrac{3}{4}} \times \Big[\Big(\dfrac{25}{9}\Big)^{-\dfrac{3}{2}} ÷ {\Big(\dfrac{5}{2}\Big)^{-3}}\Big] \\[1em] \Rightarrow \Big(\dfrac{16}{81}\Big)^{\dfrac{3}{4}} \times \Big[\Big(\dfrac{9}{25}\Big)^{\dfrac{3}{2}} ÷ {\Big(\dfrac{2}{5}\Big)^{3}}\Big] \\[1em] \Rightarrow \Big[\Big(\dfrac{2}{3}\Big)^4\Big]^{\dfrac{3}{4}} \times \Big[\Big[\Big(\dfrac{3}{5}\Big)^2\Big]^{\dfrac{3}{2}} ÷ {\Big(\dfrac{8}{125}\Big)}\Big] \\[1em] \Rightarrow \Big(\dfrac{2}{3}\Big)^3 \times \Big[\Big(\dfrac{3}{5}\Big)^3 ÷ {\Big(\dfrac{8}{125}\Big)}\Big] \\[1em] \Rightarrow \Big(\dfrac{8}{27}\Big) \times \Big[\Big(\dfrac{27}{125}\Big) ÷ {\Big(\dfrac{8}{125}\Big)}\Big] \\[1em] \Rightarrow \Big(\dfrac{8}{27}\Big) \times \Big[\Big(\dfrac{27}{125}\Big) \times {\Big(\dfrac{125}{8}\Big)}\Big] \\[1em] \Rightarrow \Big(\dfrac{8}{27}\Big) \times \Big(\dfrac{27}{8}\Big) \\[1em] \Rightarrow 1.$

Hence, $\Big(\dfrac{81}{16}\Big)^{-\dfrac{3}{4}} \times \Big[\Big(\dfrac{25}{9}\Big)^{-\dfrac{3}{2}} ÷ {\Big(\dfrac{5}{2}\Big)^{-3}}\Big] = 1$ .

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Mathematics

Evaluate the following :
$\Big(\dfrac{81}{16}\Big)^{-\dfrac{3}{4}} \times \Big[\Big(\dfrac{25}{9}\Big)^{-\dfrac{3}{2}} ÷ {\Big(\dfrac{5}{2}\Big)^{-3}}\Big]$

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Answer

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Evaluate the following :
$\sqrt{\dfrac{1}{4}} + (0.01)^{\dfrac{-1}{2}} - (27)^{\dfrac{2}{3}} \times 3^0$

Evaluate the following :
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