# How do you rewrite with fractional exponents for (root(3)(2))(root(3)(ab))?

Jun 10, 2015

$\left(\sqrt[3]{2}\right) \left(\sqrt[3]{a b}\right) = \left({2}^{\frac{1}{3}}\right) \left({\left(a b\right)}^{\frac{1}{3}}\right) \text{ or } {\left(2 a b\right)}^{\frac{1}{3}}$

#### Explanation:

SInce ${b}^{m} \cdot b \cdot n \cdot b \cdot p = {b}^{m + n + p}$
then ${b}^{\frac{1}{3}} \cdot {b}^{\frac{1}{3}} \cdot {b}^{\frac{1}{3}} = {b}^{1}$

also $\sqrt[3]{b} \cdot \sqrt[3]{b} \cdot \sqrt[3]{b} = {b}^{1}$

So $\sqrt[3]{b}$ is the same as ${b}^{\frac{1}{3}}$

Replacing $b$ with $2$ and then with $a b$ lets us derive the given solution.