# Math Help - Why are these two expressions equivalent?

1. ## Why are these two expressions equivalent?

It's always fun when math text books just instruct you to 'observe' something without explaining it.

Can someone break down for me why these two equal each other?

2. ## Re: Why are these two expressions equivalent?

If $x^6-2=0$ then you can rarrange to get $x^6 = 2$. Now take the 6th root of both sides:

$(x^6)^{1/6} = 2^{1/6}$

$(x^6)^{1/6} = x^1 = x$. This comes from the rule that $( x^a)^b = x^{(ab)}$. So you have $x = 2^{1/6}$ or $x = \sqrt[6] 2$.

Hence $\sqrt[6]2$ is a solution to $x^6-2=0$.