Need help with multiplying radicals

[Pencil]

Hi, please help me with this problem. I posted the link below. I don't understand how you get the last part. I would type it in but I don't know how to express radicals with powers with just a keyboard.



Link:
http://postimg.org/image/8xz0siyh3/

 

[pka]

Hi, please help me with this problem. I posted the link below. I don't understand how you get the last part. I would type it in but I don't know how to express radicals with powers with just a keyboard

\(\displaystyle \large \begin{align*} 4ab\sqrt[3]{a^5b^2}\cdot9a\sqrt[3]{ab^2}&=36a^2b\sqrt[3]{a^6b^4}\\&=36a^4b^2\sqrt[3]b\end{align*}\)

 

[ksdhart2]

Alright, so I'm guessing the instructions that accompanied this exercise were to simplify the given expression as much as possible. If that's the case, then the error is one in transcription. In other words, the person who wrote these steps made a typo. Everything is fine up through this step:

=36a²b(a^6/3)(b^4/3)

The next step is where the error occurs. The operation they did was valid, but what they wrote down was wrong:

=36a²b¹(a^6/3)(b¹)

What it should have been is this:

=36a²b²(a^6/3)(b^1/3)

Do you see why that is? And from there, you should also be able to see how b^1/3 becomes \(\displaystyle \displaystyle \sqrt[3]{b}\).

 

[lookagain]

\(\displaystyle 36a^4b^2\sqrt[3]3\)

\(\displaystyle 36a^4b^2\sqrt[3]b\)

 

[Pencil]

Ok I see how you got the last part. I gotta look into that more further but I guess I just need to practice more of those problems to get the big picture. Thanks