Simplify ( fourth root of x^9)/( fourth root of x^2)

$\frac{\sqrt[4]{x^{9}}}{\sqrt[4]{x^{2}}}$

Step 1

Combine $\sqrt[4]{x^{9}}$ and $\sqrt[4]{x^{2}}$ into a single radical.

$\sqrt[4]{\frac{x^{9}}{x^{2}}}$

Step 2

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{x^{9}}{x^{2}}$ by cancelling the common factors.

Factor $x^{2}$ out of $x^{9}$ .

$\sqrt[4]{\frac{x^{2} x^{7}}{x^{2}}}$

Multiply by $1$ .

$\sqrt[4]{\frac{x^{2} x^{7}}{x^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt[4]{\frac{x^{2} x^{7}}{x^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt[4]{\frac{x^{7}}{1}}$

Divide $x^{7}$ by $1$ .

$\sqrt[4]{x^{7}}$

Step 3

Factor out $x^{4}$ .

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

Step 4

Pull terms out from under the radical.

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