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Question Number 44444 by peter frank last updated on 29/Sep/18

$$simplify\sqrt{{\left(4x^{2}y\right)}^{\frac{2}{3}}+{\left(8x^2{y}^2\right)}^4}$$

Answered by tanmay.chaudhury50@gmail.com last updated on 29/Sep/18

$$\sqrt{{\left(2^2{x}^{2}y\right)}^{\frac{2}{3}}+{\left(2^3{x}^2{y}^2\right)}^4}$$$$=\sqrt{2^{\frac{4}{3}}{x}^{\frac{4}{3}}{y}^{\frac{2}{3}}+2^{12}{x}^8{y}^8}$$$$=\sqrt{2^{\frac{4}{3}}{x}^{\frac{4}{3}}{y}^{\frac{2}{3}}(1+2^{\frac{32}{3}}{x}^{\frac{20}{3}}{y}^{\frac{22}{3}})}$$$$=2^{\frac{2}{3}}{x}^{\frac{2}{3}}{y}^{\frac{1}{3}}\times \sqrt{1+2^{\frac{32}{3}}{x}^{\frac{20}{3}}{y}^{\frac{22}{3}}}$$

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