# How do you multiply 7th root of m raise to 4 times the 14th root of m raise to 9?

Jun 20, 2018

color(indigo)(=> (m)^(17/14)

#### Explanation:

${\left(\sqrt[7]{m}\right)}^{4} \cdot {\left(\sqrt[14]{m}\right)}^{9}$

Applying the theory of indices,

=> ((m^4)^(1/7) * ((m^9)^(1/14))

$\implies . {\left(m\right)}^{\frac{4}{7}} \cdot {\left(m\right)}^{\frac{9}{14}}$

$\implies {\left(m\right)}^{\frac{4}{7} + \frac{9}{14}}$

$\implies {\left(m\right)}^{\frac{8 + 9}{14}}$

color(indigo)(=> (m)^(17/14)