Step 1

Use this formula to solve:

\(\sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\) The product rule for radicals,

\(\sqrt[n]{a}=a^{1/n}\) The relation between radical and rational exponent notation is expressed as.

Step 2

Use the prodict rule for radicals to simplify the expression,

\(\displaystyle{a}\div\sqrt{{{b}}}={\frac{{{a}}}{{\sqrt{{{b}}}}}}\)

\(\displaystyle={\frac{{{a}}}{{\sqrt{{{b}}}}}}\times{\frac{{\sqrt{{{b}}}}}{{\sqrt{{{b}}}}}}\)

\(\displaystyle={\frac{{{a}\sqrt{{{b}}}}}{{{\left(\sqrt{{{b}}}\right)}^{{{2}}}}}}\)

Use the relation between radical and rational exponent notation to simplify the expression,

\(\displaystyle{a}\div\sqrt{{{b}}}={\frac{{{a}\sqrt{{{b}}}}}{{{\left({b}^{{\frac{{1}}{{2}}}}\right)}^{{{2}}}}}}\)

\(\displaystyle={\frac{{{2}\sqrt{{{b}}}}}{{{\left({b}\right)}^{{{2}{\left(\frac{{1}}{{2}}\right)}}}}}}\)

\(\displaystyle={\frac{{{a}\sqrt{{{b}}}}}{{{b}}}}\)

Hence, the simplified value of the provided expression is \(\displaystyle{\frac{{{a}\sqrt{{{b}}}}}{{{b}}}}\)