Write in Exponential Form ( square root of a square root of b)/( ninth root of ab)

$\frac{\sqrt{a \sqrt{b}}}{\sqrt[9]{a b}}$

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

$\frac{\sqrt{a b^{\frac{1}{2}}}}{\sqrt[9]{a b}}$

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

$\frac{{(a b^{\frac{1}{2}})}^{\frac{1}{2}}}{\sqrt[9]{a b}}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[9]{a b}$ as ${(a b)}^{\frac{1}{9}}$ .

$\frac{{(a b^{\frac{1}{2}})}^{\frac{1}{2}}}{{(a b)}^{\frac{1}{9}}}$