Question

How do I find the radical form of this expression
I will write it how it is
Please explain slowly will fan and metal

Answer 1

\[(32a ^{10}b ^{5 \over 2})^{2 \over 5}\]

Answer 2

Anyone know how to solve?

Answer 3

When you have a "fraction" or "rational" exponent,
example: \(\large\rm x^{m/n}\)

The numerator of this fraction represents the "power" as you're used to,
while the denominator represents the degree of the "root"
so in that example, I could rewrite it in this form: \(\large\rm \sqrt[n]{x^m}\)

Answer 4

Okay

Answer 5

So in your problem, we're focusing on the outermost exponent.
The numerator is a 2, the "power" on the expression.
while the denominator is a 5, the degree of our "root".

Answer 6

Okay so it would make the answer A. but please continue

Answer 7

i'd like to learn

Answer 8

Good, option A :)

\(\large\rm (stuff)^{2/5}=\sqrt[5]{(stuff)^2}\)

Answer 9

Okay because the fraction outside the parenthesis would make up the radical?

Answer 10

Outside the parenthesis?
Well, only the denominator of that fraction is giving us the radical :)


It becomes a little more tricky when they give you a 1 in the numerator.
Realize that that represents a 1 "power", which is insignificant,
so it really only represents a root.

Example: \(\large\rm (stuff)^{1/2}=\sqrt[2]{(stuff)^1}=\sqrt{stuff}\)
We'll relate this to the last problem in just a sec.

Answer 11

Okay

Answer 12

I'm not sure if you've learned all of your exponent rules at this point,
but here is one of them,\[\large\rm (a^b)^c=a^{bc}\]In your original problem,
we can actually apply this rule in reverse,\[\large\rm (stuff)^{2/5}=(stuff)^{2\cdot\frac{1}{5}}=\left[(stuff)^2\right]^{1/5}=\sqrt[5]{(stuff)^2}\]If that's way too complicated, you can ignore it for now :)
Just another way to understand where this weird change from fraction to root is coming from.

Answer 13

Okay ill keep that in mind actually

Answer 14

Hmm I'm not sure what else we could say about this XD

Answer 15

Thats fine im stuck on a new problem lol