Exponential Form of Radicals
A radical can be expressed in exponential form by using the equivalence:
[tex]\sqrt[m]{x^n}=x^{\frac{n}{m}}[/tex]
We are given the expression:
[tex]\sqrt[4]{16a^4b^3}[/tex]
It can be separated into several radicals:
[tex]\sqrt[4]{16a^4b^3}=\sqrt[4]{16}\cdot\sqrt[4]{a^4}\cdot\sqrt[4]{b^3}[/tex]
Now we apply the equivalence on each individual radical:
[tex]\begin{gathered} \sqrt[4]{16a^4b^3}=\sqrt[4]{2^4}\cdot\sqrt[4]{a^4}\cdot\sqrt[4]{b^3} \\ \sqrt[4]{16a^4b^3}=2^{\frac{4}{4}}\cdot a^{\frac{4}{4}}\cdot b^{\frac{3}{4}} \end{gathered}[/tex]
Simplifying:
[tex]\sqrt[4]{16a^4b^3}=2ab^{\frac{3}{4}}[/tex]
