can someone help me figure this out: 10√a5b5?

Question

I have to use rational exponents to simplify the radical

Answer 1

[01]
10sqrt(a^5 b^5)
=10sqrt(a^4b^4[ab])
=10a^2b^2 sqrt(ab)

Answer 2

I'm assuming you mean a^5 b^5 under the radical.

This can be written as a^1 a^2 a^2 b^1 b^2 b^2 under the radical. sqrt a^2 becomes a and so on. You will end up with 10a^2b^2 times sqrt ab

Answer 3

I assume you meant to type a^5 and b^5.

We have this:

10(sqrt{a^5b^5})

We "house" the square roots separately and simplify.

sqrt{a^5} and sqrt{b^5}

We now need to simplify each radical by multiplying a and b times a perfect square separately.

sqrt{a^5} = sqrt{a times a^4}. where a^4 is our perfect square because a^2 times a^2 = a^4. I assume you know the definition of perfect square, right?

Then sqrt{a^5} becomes a^2(sqrt{a})

We now do the same to the other radical ending up with
b^2(sqrt{b})

We now put it all together and done!

Here is your final answer:

10(a^2)(b^2) times sqrt{ab}

Answer 4

I kinda wish I knew what "rational exponents" were
(on 2nd thoughts ...I'm happier not knowing lol)

on that expression only the 5 can be removed
to give 50√ab

so any way you dress it it's 50 times a^0.5 times b^0.5

I answered the question as it was submitted
(you get nil points for answering a hypothetical question)
it does NOT say a^5 or b^5

Answer 5

10 sqrt a^5b^5

a^4b^4 can be taken out so I would say 10a^2b^2 sqrt of ab