# How do you simplify (\root [ 11] { 9x ^ { 6} y } ) ^ { 7}?

Apr 20, 2018

$\text{ }$
color(brown)((\root [ 11] { 9x ^ { 6} y } ) ^ { 7}= [9^(7/11)][x^(42/11)][y^(7/11)]

#### Explanation:

$\text{ }$
We have color(red)((\root [ 11] { 9x ^ { 6} y } ) ^ { 7}

Useful Exponent formula:

color(blue)((a^m)^n = a^(mn)

color(blue)(root(n)m = m^(1/n)

color(blue)(root(n)(a^m) = a^(m/n)

Consider:

${\left(\setminus \sqrt[11]{9 {x}^{6} y}\right)}^{7}$ given expression

Simplify this expression using the formula list above.

${\left[\sqrt[11]{9} \cdot \sqrt[11]{{x}^{6}} \cdot \sqrt[11]{y}\right]}^{7}$

$\Rightarrow {\left[\sqrt[11]{{9}^{1}} \cdot \sqrt[11]{{x}^{6}} \cdot \sqrt[11]{{y}^{1}}\right]}^{7}$

$\Rightarrow {\left[{9}^{\frac{1}{11}} \cdot {x}^{\frac{6}{11}} \cdot {y}^{\frac{1}{11}}\right]}^{7}$

$\Rightarrow {9}^{\frac{7}{11}} \cdot {x}^{\frac{42}{11}} \cdot {y}^{\frac{7}{11}}$

Hence,

color(brown)((\root [ 11] { 9x ^ { 6} y } ) ^ { 7}= [9^(7/11)][x^(42/11)][y^(7/11)]

Hope it helps.