Simplify the Radical Expression square root of 1/(h^-5*h^6)

$\sqrt{\frac{1}{h^{- 5} \cdot h^{6}}}$

Multiply $h^{- 5}$ by $h^{6}$ by adding the exponents.

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

$\sqrt{\frac{1}{h^{- 5 + 6}}}$

Add $- 5$ and $6$ .

$\sqrt{\frac{1}{h^{1}}}$

Simplify $h^{1}$ .

$\sqrt{\frac{1}{h}}$

Rewrite $\sqrt{\frac{1}{h}}$ as $\frac{\sqrt{1}}{\sqrt{h}}$ .

$\frac{\sqrt{1}}{\sqrt{h}}$

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{h}}$

Multiply $\frac{1}{\sqrt{h}}$ by $\frac{\sqrt{h}}{\sqrt{h}}$ .

$\frac{1}{\sqrt{h}} \cdot \frac{\sqrt{h}}{\sqrt{h}}$

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{h}}$ by $\frac{\sqrt{h}}{\sqrt{h}}$ .

$\frac{\sqrt{h}}{\sqrt{h} \sqrt{h}}$

Raise $\sqrt{h}$ to the power of $1$ .

$\frac{\sqrt{h}}{{\sqrt{h}}^{1} \sqrt{h}}$

Raise $\sqrt{h}$ to the power of $1$ .

$\frac{\sqrt{h}}{{\sqrt{h}}^{1} {\sqrt{h}}^{1}}$

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

$\frac{\sqrt{h}}{{\sqrt{h}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{h}}{{\sqrt{h}}^{2}}$

Rewrite ${\sqrt{h}}^{2}$ as $h$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{h}$ as $h^{\frac{1}{2}}$ .

$\frac{\sqrt{h}}{{(h^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{h}}{h^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{\sqrt{h}}{h^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{h}}{h^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{h}}{h^{1}}$

Simplify.

$\frac{\sqrt{h}}{h}$