Simplify the Radical Expression sixth root of (g^6h)/(h^7)

$\sqrt[6]{\frac{g^{6} h}{h^{7}}}$

Step 1

Reduce the expression $\frac{g^{6} h}{h^{7}}$ by cancelling the common factors.

Factor $h$ out of $g^{6} h$ .

$\sqrt[6]{\frac{h g^{6}}{h^{7}}}$

Factor $h$ out of $h^{7}$ .

$\sqrt[6]{\frac{h g^{6}}{h \cdot h^{6}}}$

Cancel the common factor.

$\sqrt[6]{\frac{h g^{6}}{h \cdot h^{6}}}$

Rewrite the expression.

$\sqrt[6]{\frac{g^{6}}{h^{6}}}$

Step 2

Rewrite $\frac{g^{6}}{h^{6}}$ as ${(\frac{g}{h})}^{6}$ .

$\sqrt[6]{{(\frac{g}{h})}^{6}}$

Step 3

Pull terms out from under the radical.

$| \frac{g}{h} |$