8x^3*y^-2*z^-4 divided by 6x^-1*yz^-5

Question

4n1m0s1ty · Answer

Is this what you are trying to solve?

$$\frac{8x^{3}y^{-2}z^{-4}}{6x^{-1}yz^{-5}}$$

anonymous · Answer

yes 4n1m0s1ty it is

anonymous · Answer

if you could also explain what medals are and what I can do with one I will give one to you if I can.  Unless I have to get one first in which case I don't have one.

4n1m0s1ty · Answer

Jsut hit the best response button, and it will give me a medal. Medals are kind of like the reward system on this site. You give medals to people who help you out!

Anyways, are you familiar with what the negative exponent does? It flips the term it is attached to numerator/denomenator from opposite side. For example:

$$\frac{x^{-1}}{1} = \frac{1}{x}$$

Make sense? So, what terms can we flip to the opposite side in this problem?

anonymous · Answer

we can flip the y^-2 and the z^-4 on the top and the 6x^-1 and yz^-5 (or do we not flip the y along with the z^-5 on the last one?)

4n1m0s1ty · Answer

You are right about the top terms. y and z^-5 are two different terms so you would just flip the z by itself.

So now we have this:
$$\frac{8x^{3}x^{1}z^{5}}{6yy^{2}z^{4}}$$

We combine exponents with terms of similar base multiplied together. For example:

$$x^{2}x^{6}=x^{8}$$
or 
$$y^{4}y^{7}=y^{11}$$

Now what can we combine in this problem?

anonymous · Answer

we can combine 8x^3 and x^1 to get 8x^4 and we can combine 6y and y^2 to get 6y^3

4n1m0s1ty · Answer

Yep, so now we have this:

$$\frac{8x^{4}z^{5}}{6y^{3}z^{4}}$$

We can do the opposite to exponents when the bases are being divided. Instead of adding, we subtract, for example:

$$\frac{z^{6}}{z^{4}}=\frac{z^{2}}{1}$$

or

$$\frac{z^{5}}{z^{7}}=\frac{z^{-2}}{1}=\frac{1}{z^{2}}$$

So, which term(s) can we do this to?

anonymous · Answer

we can subtract z^4 from z^5 and get plain old z on the numerator

4n1m0s1ty · Answer

Yep, so now we have this:

$$\frac{8x^{4}z}{6y^{3}}$$

the only thing left to do is simplify 8/3 to a simpler fraction, and you are left with the answer. What does 8/6 simplify down to?

4n1m0s1ty · Answer

I meant to say 8/6 not 8/3.

anonymous · Answer

ok so we are left with  $$4x^4z/6y^3$$

anonymous · Answer

wait not 6 i meant 3

4n1m0s1ty · Answer

yep thats right. I was about to correct you for a moment when you said 3.

You've found the answer. Just need to remember those rules when you solve these types of problems.

4n1m0s1ty · Answer

im mean 6. too many numbers today...

anonymous · Answer

thanks you were a lot of help :)

4n1m0s1ty · Answer

no problem