Simplify ( cube root of 64x^3y)/(4x^-3y)

$\frac{\sqrt[3]{64 x^{3} y}}{4 x^{- 3} y}$

Step 1

Move $x^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{\sqrt[3]{64 x^{3} y} x^{3}}{4 y}$

Step 2

Simplify the numerator.

Rewrite $64 x^{3} y$ as ${(4 x)}^{3} y$ .

Rewrite $64$ as $4^{3}$ .

$\frac{\sqrt[3]{4^{3} x^{3} y} x^{3}}{4 y}$

Rewrite $4^{3} x^{3}$ as ${(4 x)}^{3}$ .

$\frac{\sqrt[3]{{(4 x)}^{3} y} x^{3}}{4 y}$

Pull terms out from under the radical.

$\frac{4 x \sqrt[3]{y} x^{3}}{4 y}$

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{4 (x^{3} x) \sqrt[3]{y}}{4 y}$

Multiply $x^{3}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{4 (x^{3} x^{1}) \sqrt[3]{y}}{4 y}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 x^{3 + 1} \sqrt[3]{y}}{4 y}$

Add $3$ and $1$ .

$\frac{4 x^{4} \sqrt[3]{y}}{4 y}$

Step 3

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{4} \sqrt[3]{y}}{4 y}$

Rewrite the expression.

$\frac{x^{4} \sqrt[3]{y}}{y}$