Answer:
[tex]\sqrt[7]{3^{2}}[/tex]
Step-by-step explanation:
[tex]3^{2/7}[/tex]
^ 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 [tex]2^{1/2}[/tex]. That is the same exact thing as saying [tex]\sqrt{2}[/tex]. It's the same thing. You can say it either way.
In the same way, a squared power, like [tex]2^{2}[/tex], is the same as representing it like a fraction, like [tex]2^{2/1}[/tex]. 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.
[tex]3^{2/7}[/tex]
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: [tex]3^{2}[/tex].
And since we have a fraction that's also included, we now know that is a root. So we can represent that like this: [tex]\sqrt[7]{3}[/tex].
But those two answers need to be combined. We can do that like this: [tex]\sqrt[7]{3^{2}}[/tex]
Answer: [tex]\sqrt[7]{3^{2}}[/tex]
So there it is! I hope that helped you!!
