# How do you simplify (7x^2yz)^3?

Jul 18, 2017

$= 343 {x}^{6} {y}^{3} {z}^{3}$

#### Explanation:

The index shown applies to all the factors inside the bracket.

Recall the laws of indices:

${\left(x y z\right)}^{m} = {x}^{m} {y}^{m} {z}^{m} \text{ and } {\left({x}^{m}\right)}^{n} = {x}^{m n}$

Using both of these laws gives:

${\left(7 {x}^{2} y z\right)}^{3} = {7}^{3} {x}^{6} {y}^{3} {z}^{3}$

While ${7}^{3}$ is acceptable, you might want to find the actual value.

${7}^{3} {x}^{6} {y}^{3} {z}^{3}$

$= 343 {x}^{6} {y}^{3} {z}^{3}$