What is (\sqrt[3]{48x^3y^2})/(\sqrt[3]{6x^4y)} ?

The solution to (\sqrt[3]{48x^3y^2})/(\sqrt[3]{6x^4y)} is (2\sqrt[3]{y})/(\sqrt[3]{x)}

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simplify (\sqrt[3]{48x^3y^2})/(\sqrt[3]{6x^4y)}

simplify

\frac{3 48 x ^{3} y ^{2}}{3 6 x ^{4} y}

\frac{2 3 y}{3 x}

Solution steps

\frac{3 48 x ^{3} y ^{2}}{3 6 x ^{4} y}

Apply radical rule:

\frac{n a}{n b} = n \frac{a}{b},

assuming

a \geq 0, b \geq 0

\frac{3 48 x ^{3} y ^{2}}{3 6 x ^{4} y} = 3 \frac{48 x ^{3} y ^{2}}{6 x ^{4} y}

= 3 \frac{48 x ^{3} y ^{2}}{6 x ^{4} y}

Cancel

\frac{48 x ^{3} y ^{2}}{6 x ^{4} y} : \frac{8 y}{x}

= 3 \frac{8 y}{x}

Apply radical rule:

n \frac{a}{b} = \frac{n a}{n b},

assuming

a \geq 0, b \geq 0

= \frac{3 8 y}{3 x}

Simplify

3 8 y : 2 3 y

= \frac{2 3 y}{3 x}

4 - 5 y = - 1

3 x^{2} + 16 x - 10 = 6 x - 2

- 3 x^{2} + 2 x + 5

\frac{16}{49}

8 1^{- \frac{3}{4}}

What is (\sqrt[3]{48x^3y^2})/(\sqrt[3]{6x^4y)} ?
The solution to (\sqrt[3]{48x^3y^2})/(\sqrt[3]{6x^4y)} is (2\sqrt[3]{y})/(\sqrt[3]{x)}