Simplify, evaluate (2^2 x^5 y^-3 z^4 / 4^0 x^-2 y^-8 z^5)^3

[Math illiterate]

I need to simplify and evaluate this problem. I have no clue how to even begin this problem.

(2[sup:1fiqv2bp]2[/sup:1fiqv2bp]x[sup:1fiqv2bp]5[/sup:1fiqv2bp]y[sup:1fiqv2bp]-3[/sup:1fiqv2bp]z[sup:1fiqv2bp]4[/sup:1fiqv2bp]/4[sup:1fiqv2bp]0[/sup:1fiqv2bp]x[sup:1fiqv2bp]-2[/sup:1fiqv2bp]y[sup:1fiqv2bp]-8[/sup:1fiqv2bp]z[sup:1fiqv2bp]5[/sup:1fiqv2bp])[sup:1fiqv2bp]3[/sup:1fiqv2bp]

 

[Loren]

Re: Simplify and evaluate:

Technically speaking (2[sup:3dx56ux5]2[/sup:3dx56ux5]x[sup:3dx56ux5]5[/sup:3dx56ux5]y[sup:3dx56ux5]-3[/sup:3dx56ux5]z[sup:3dx56ux5]4[/sup:3dx56ux5]/4[sup:3dx56ux5]0[/sup:3dx56ux5]x[sup:3dx56ux5]-2[/sup:3dx56ux5]y[sup:3dx56ux5]-8[/sup:3dx56ux5]z[sup:3dx56ux5]5[/sup:3dx56ux5])[sup:3dx56ux5]3[/sup:3dx56ux5] means \(\displaystyle \left(\frac{2^2x^5y^{-3}z^4}{4^0}\cdot x^{-2}y^{-8}z^5\right)^3\)

I think you mean (2[sup:3dx56ux5]2[/sup:3dx56ux5]x[sup:3dx56ux5]5[/sup:3dx56ux5]y[sup:3dx56ux5]-3[/sup:3dx56ux5]z[sup:3dx56ux5]4[/sup:3dx56ux5]/(4[sup:3dx56ux5]0[/sup:3dx56ux5]x[sup:3dx56ux5]-2[/sup:3dx56ux5]y[sup:3dx56ux5]-8[/sup:3dx56ux5]z[sup:3dx56ux5]5[/sup:3dx56ux5]))[sup:3dx56ux5]3[/sup:3dx56ux5] which is

\(\displaystyle \left(\frac{2^2x^5y^{-3}z^4}{4^0x^{-2}y^{-8}z^5}\right)^3\)

You need to use (and memorize) the laws of exponents.

\(\displaystyle x^a\cdot x^b = x^{a+b}\)

\(\displaystyle \frac{x^a}{x^b}=x^{a-b)\)

\(\displaystyle (x^a)^b =x^{ab}\)

Also,
\(\displaystyle x^0 = 1\)

and

\(\displaystyle x^n = x\cdot x\cdot x\cdot x...\) n times, or in other words, x taken as a factor n times.

I believe those are all you need to get your answer. Order of using them makes no difference.

 

[tkhunny]

Re: Simplify and evaluate:

Ah, my favorite...

1) Change you screen name and stop beating yourself up. Also, quit listenign to anyone else who talks about you in this manner.

2) You can't possibly have no clue if you ahve been to class once or cracked the book open once or heard three words form the teachers mouth or seen one screen on the overhead. you MUST have SOME clue.

3) you need only the rules of exponents to solve this one.

For 'a' NOT zero, we have:

a^m / a^n = a^(m-n)

Example x^2 / x^3 = x^(2-3) = x^(-1)

For a^(-n) = 1/(a^n)

Example: a^(-2) = 1/(a^2)

Notice how the base is the same or this does not work.

Example: a^3 / b^2 = a^3 / b^2 -- The bases are not the same. 2 is not 3. Leave it alone.

Once in a while, they will sneak one in on you and a little effort will track it down.

2^2 / 4^2 = Can't do it, rght? The bases are not the same. 2 is NOT equal to 4. Well, in this case, one might obsere that the bases are strongly related.

4 = 2*2 = 2^2

2^2 / 4^2 = 2^2 / (2^2)^2 = 2^2 / 2^4 = 2^(2-4) = 2^(-2) = 1/(2^2) = 1/4

Okay. That's about all you need. Now give it a shot.