Let's say you have y = x^{m/n} Let's say for the sake of argument, you want to get rid of the "n" in the denominator. I was shown a technique to do so, but I don't understand as to how it is possible. * Raise both sides to the power "n" ^ how could you do this? y^{n} = x^{m/n*(n)} y^{n} = x^{m}

first do you remember law of exponents \[(x^r)^s=x^{r \cdot s}\]

\[y=x^\frac{m}{n}\] \[y^n=(x^\frac{m}{n})^n\]

\[y^n=x^{(\frac{m}{n} \cdot n)}\]

Which law of exponents is this?

Ok so this law allows you to raise a power on both sides without having a base?

\[y^n=x^\frac{m \cdot n}{n} \] \[y^n=x^\frac{m \not {n}}{\not{n}}\] \[y^n=x^\frac{m}{1}\] \[y^n=x^m\]

no we do have bases on the same side

if i told you \[8=2^3\] which is true does \[8^\frac{1}{3}=(2^3)^\frac{1}{3}\]

?

forgot the question mark

So you can tack on a power to both sides, without accompanying it with a base. I am not saying it is going there without a base.

if i say something is equal to something, and i raise both sides to some power they are till going to be equal

of course those powers that i raise both sides to have to be the same power

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