# How do you simplify (2x^6^m)/(6x^2^m)?

Jul 1, 2015

${\left(\frac{{x}^{4}}{3}\right)}^{m} \mathmr{if} x \in \mathbb{R} - \left\{0\right\} , m \in \mathbb{R}$

#### Explanation:

Step 1 : The domain of the function.

We have only one forbidden value, when $x = 0$. This is the only value where your denominator equal 0. And we can't divide by 0...

Therefore, the domain of our function is : $\mathbb{R} - \left\{0\right\}$ for $x$ and $\mathbb{R}$ for $m$.

Step 2 : Factoring power m

$\frac{2 {x}^{6} ^ m}{6 {x}^{2} ^ m}$ <=> ${\left(2 {x}^{6}\right)}^{m} / {\left(6 {x}^{2}\right)}^{m}$ <=> ${\left(\frac{2 {x}^{6}}{6 {x}^{2}}\right)}^{m}$

Step 3 : Simplify the fraction

${\left(\frac{2 {x}^{6}}{6 {x}^{2}}\right)}^{m}$ <=> ${\left(\frac{{x}^{6}}{3 {x}^{2}}\right)}^{m}$ <=> ${\left(\frac{{x}^{4}}{3}\right)}^{m}$

Don't forget, $x \ne 0$