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}

Question

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}

myininaya · Answer

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

myininaya · Answer

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

myininaya · Answer

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

anonymous · Answer

Which law of exponents is this?

anonymous · Answer

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

myininaya · Answer

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

myininaya · Answer

no we do have bases on the same side

myininaya · Answer

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

myininaya · Answer

?

myininaya · Answer

forgot the question mark

anonymous · Answer

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.

myininaya · Answer

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

myininaya · Answer

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