[( 25 9 )^ 5 2 #160; ]^ 3 5 #160; =[ [( 5 3 )^ 2 ]^ 5 2 #160; ]^ 3 5 #160; =[( 5 3 )^ 5 ]^ 3 5 #160; =( 5 3 )^ ...

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Particular Solution of a Differential Equation

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Question

Simplify: ${⎡ ⎢ ⎢ ⎣ {(\frac{25}{9})}^{\frac{5}{2}} ⎤ ⎥ ⎥ ⎦}^{\frac{3}{5}}$

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Solution

$[(\frac{25}{9})^{\frac{5}{2}}]^{\frac{3}{5}} = [[(\frac{5}{3})^{2}]^{\frac{5}{2}}]^{\frac{3}{5}} = [(\frac{5}{3})^{5}]^{\frac{3}{5}} = (53)^{3} = \frac{125}{27}$

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Similar questions

⎡ ⎢ ⎢ ⎣ {(\frac{25}{9})}^{\frac{- 3}{2}} \div {(\frac{5}{3})}^{- 3} ⎤ ⎥ ⎥ ⎦

{(\frac{2}{5})}^{- 3} \times {(\frac{25}{4})}^{- 2}

\frac{5 + \sqrt{3}}{5 - \sqrt{3}} + \frac{5 - \sqrt{3}}{5 + \sqrt{3}}

\frac{1}{2 + \sqrt{3}} + \frac{2}{\sqrt{5} - \sqrt{3}} + \frac{1}{2 - \sqrt{5}}

\frac{2}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{2}} + \frac{3}{\sqrt{5} + \sqrt{2}}

Simplify : 25-1/2{5+4-(3+2-1+3)}

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