How to simplify $3 \sqrt[n]{x^{2 n + 1} y^{3 n}}$ $3root(n)(x^(2n+1)y^(3n)$ ?

Question

$3 \sqrt[n]{x^{2 n + 1} y^{3 n}}$ $3root(n)(x^(2n+1)y^(3n)$

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Answer 1 · 2018-02-24T10:20:34

Given expression can be written as,

$3 {(x^{2 n + 1} y^{3 n})}^{\frac{1}{n}}$ $3 (x^(2n+1) y^(3n))^(1/n)$

$= 3 x^{(2 n + 1) (\frac{1}{n})} y^{(3 n) (\frac{1}{n})}$ $= 3 x^((2n+1)(1/n)) y^((3n)(1/n))$

$= 3 x^{(\frac{2 n + 1}{n})} y^{3}$ $= 3 x^(((2n+1)/n)) y^3$