Product of Two Algebric Expressions with Exponents.

[EnjoyablyC]

Hello everyone. English is not my first language so I tried translating the terms as best I could. I'm having a lot of issue with this and I'm starting to get a bit depressed since I'm just so hopelessly in need of help. I just need one solid example with a small explanation of each step to understand it.

Here is the problem:

(18^1/2 / 12^3/4)^4 ÷ (27^1/3 / 8^1/2)^-4

**An important thing to note is that they want me to have the answer without any negative exponents.**

Here is a picture I took of it, in case above to too complicated to follow.

<Name Removed> LINK:

​< link to objectionable page removed >

(the exponent on the left fraction is 4 and on the right is -4 in case you can't see clearly)

**An important thing to note is that they want me to have the answer without any negative exponents.**

Okay, now I'd love to show you guys what I did but unfortunately I really just don't have any idea what the heck I should do. I vaguely remember something about simplifying the bases but I don't quite remember how they want me to do it. I tried doing this and was left with:

(2⁴ 3² / 2⁶ 3³⁾ ÷ (3^-4 / 2⁶⁾

But I'm not really sure where to do after this.

I feel really scummy asking this but I really just need someone to show me what to do. Thank you for reading this, and if you don't feel like helping me I understand.

I know the answer is: 3^5 / 2^10

 

[EnjoyablyC]

Your English is quite good...better than mine!

Your expression should have the fractional powers bracketed:

[18^(1/2) / 12^(3/4)]^4 ÷ [27^(1/3) / 8^(1/2)]^-4

Good news: above can be changed right away to:

[18^(1/2) / 12^(3/4)]^4 * [27^(1/3) / 8^(1/2)]^4

You seem to be unaware of the basic exponent rules;
suggest you go here:
http://www.mathsisfun.com/algebra/exponent-laws.html

You will see why your expression can be changed to what I show above,
plus you will become familiar with the basic rules (and see how simple they are!).

Give it another shot, and come back if you have questions...GOOD LUCK.

Note:
your problem should be worded:
"simplification of algebraic expression", not "product....."

Sorry for not having replied sooner, but now that its expressed as

[18^(1/2) / 12^(3/4)]^4 * [27^(1/3) / 8^(1/2)]^4

I have no problem solving it. It's much easier in that format. Thanks, man!