Question

PLEASE HELP ME!! write three to the power of two sevenths in radical form and explain?

Answer 1

Answer:

4782969

Step-by-step explanation:

Answer 2

Answer:

$\sqrt[7]{3^{2}}$

Step-by-step explanation:

$3^{2/7}$

^ That is 3 to the 2/7ths power. We know that. Now it needs to be in radical form. That takes a bit of thinking.

If you have a power that is less than one (like 1/2) it is can be written as a root. So say you're given $2^{1/2}$. That is the same exact thing as saying $\sqrt{2}$. It's the same thing. You can say it either way.

In the same way, a squared power, like $2^{2}$, is the same as representing it like a fraction, like $2^{2/1}$. They both mean the same thing.

So by pointing these out, a fraction power = the power / the root.

If that makes sense.

So, with this in mind, let's look at what we have again.

$3^{2/7}$

So we can split it up to say that 3 is raised to a 2nd power times a 1/7th power.

So we know what a 3 to the 2nd power is: $3^{2}$.

And since we have a fraction that's also included, we now know that is a root. So we can represent that like this: $\sqrt[7]{3}$.

But those two answers need to be combined. We can do that like this: $\sqrt[7]{3^{2}}$

Answer: $\sqrt[7]{3^{2}}$

So there it is! I hope that helped you!!