# How do you simplify (-3^(2/3))(4^(1/4))?

May 31, 2017

$\left(- {3}^{\frac{2}{3}}\right) \left({4}^{\frac{1}{4}}\right) = - \sqrt[12]{419904} = - 2.9417$

#### Explanation:

In fractional exponents we have $3$ and $4$ as denominators. So let us reduce them to common denominators i.e. $12$ as $12$ is GCD of $3$ and $4$. Hence

$\left(- {3}^{\frac{2}{3}}\right) \left({4}^{\frac{1}{4}}\right)$

= $\left(- {3}^{\frac{2 \times 4}{3 \times 4}}\right) \left({4}^{\frac{1 \times 3}{4 \times 3}}\right)$

= $\left(- {3}^{\frac{8}{12}}\right) \left({4}^{\frac{3}{12}}\right)$

= ${\left(- {3}^{8} \times {4}^{3}\right)}^{\frac{1}{12}}$

= ${\left(- 6561 \times 64\right)}^{\frac{1}{12}}$

= $- \sqrt[12]{419904}$

Incidentally, it is equal to $- 2.9417$