What is (\sqrt[7]{6xsqrt(3y)})^3 ?

The solution to (\sqrt[7]{6xsqrt(3y)})^3 is 6^{3/7}(sqrt(3)xsqrt(y))^{3/7}

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simplify (\sqrt[7]{6xsqrt(3y)})^3

simplify

6^{\frac{3}{7}} (3 x y)^{\frac{3}{7}}

Solution steps

Apply radical rule:

= ((6 x 3 y)^{\frac{1}{7}})^{3}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (6 x 3 y)^{\frac{1}{7} \cdot 3}

\frac{1}{7} \cdot 3 = \frac{3}{7}

= (6 x 3 y)^{\frac{3}{7}}

3 y = 3 y

= (63 x y)^{\frac{3}{7}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 6^{\frac{3}{7}} (3 x y)^{\frac{3}{7}}

(17.8508 \cdot 1 0^{- 6}) (- 13461)

(3 a^{x - 2}) (2 a)

(6 b^{3}) (3 b^{4})

5.61 \cdot 1 0^{- 4}

What is (\sqrt[7]{6xsqrt(3y)})^3 ?
The solution to (\sqrt[7]{6xsqrt(3y)})^3 is 6^{3/7}(sqrt(3)xsqrt(y))^{3/7}