Simplify :
(8x3÷125y3)23(8x^3 ÷ 125y^3)^{\dfrac{2}{3}}(8x3÷125y3)32
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Simplifying the expression :
⇒(8x3125y3)23=[(2x)3(5y)3]23=[(2x5y)3]23=(2x5y)2=4x225y2.\Rightarrow \Big(\dfrac{8x^3}{125y^3}\Big)^{\dfrac{2}{3}} =\Big[\dfrac{(2x)^3}{(5y)^3}\Big]^{\dfrac{2}{3}} \\[1em] = \Big[\Big(\dfrac{2x}{5y}\Big)^3\Big]^{\dfrac{2}{3}} = \Big(\dfrac{2x}{5y}\Big)^2 \\[1em] = \dfrac{4x^2}{25y^2}.⇒(125y38x3)32=[(5y)3(2x)3]32=[(5y2x)3]32=(5y2x)2=25y24x2.
Hence, (8x3÷125y3)23=4x225y2.(8x^3 ÷ 125y^3)^{\dfrac{2}{3}} = \dfrac{4x^2}{25y^2}.(8x3÷125y3)32=25y24x2.
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Evaluate :
70×(25)−32−5−37^0 \times (25)^{-\dfrac{3}{2}} - 5^{-3}70×(25)−23−5−3
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(a + b)-1.(a-1 + b-1)
5n+3−6×5n+19×5n−5n×22\dfrac{5^{n + 3} - 6 \times 5^{n + 1}}{9 \times 5^n - 5^n \times 2^2}9×5n−5n×225n+3−6×5n+1
