How would I Simplify this?

[Blue23]

I was having some trouble with this question.

Simplify: 2^2(x-1)^-2(x^2 y)^3/√4x^6 (x-1)^2 y^-2

If you could show me step by step how it should be worked out and explain why you did what you did in each step that would be great.

Thanks a heap.

 

[stapel]

Simplify: 2^2(x-1)^-2(x^2 y)^3/√4x^6 (x-1)^2 y^-2

Just to clarify, I think that your meaning is as follows:

\(\displaystyle \displaystyle{\frac{2^2 (x\, -\, 1)^{-2} (x^2 y)^3} {\sqrt{4x^6} (x\, -\, 1)^2 y^{-2}}}\)

If you could show me step by step how it should be worked out and explain why you did what you did in each step that would be great.

You already have loads of worked and explained examples in your book and in your class notes. If they aren't helping, then another example probably won't, either. So please write back, confirming or correcting my assumed meaning above and also showing your work so far. Once we can see what you're doing, we can provide useful instructions. Thank you!

 

[HallsofIvy]

What you need are the "rules of exponents": \(\displaystyle a^xa^y= a^{x+y}\), \(\displaystyle \frac{a^x}{a^y}= a^{x- y}\), and \(\displaystyle (a^x)^y= a^{xy}\).

Combine terms that have the same base and use those.

 

[Blue23]

Hi Stapel,

you are right I'm trying to simplify


[FONT=MathJax_Main]2[FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]√[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]2[/FONT][/FONT]


This is what I've got so far:

[FONT=MathJax_Main]2[FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]√[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]2[/FONT][/FONT]

= 2²(x^-2+1) (x⁶y³) / [FONT=MathJax_Main]√4x⁶ (x[/FONT][FONT=MathJax_Main]²+1)y^-2
[/FONT]
= 4(x^-2+1) (x⁶y³) / [FONT=MathJax_Main]√4x⁶ (x[/FONT][FONT=MathJax_Main]²+1)y^-2
[/FONT]
= (4x^-2+4) (x⁶y³) / [FONT=MathJax_Main]√4x⁶ (x[/FONT][FONT=MathJax_Main]²+1)y^-2
[/FONT]
= 4x⁴+4x^-2y³+4x⁶+4y³ / [FONT=MathJax_Main]√4x⁶ (x[/FONT][FONT=MathJax_Main]²+1)y^-2
[/FONT]
= 4x⁴+4x^-2y³+4x⁶+4y³ / 4x⁶+4x⁴+y^-2


Thats what I've got so far not sure if its right or wrong.
If you could please show me step by step how it should be worked out I'm sure I'd understand it better.

Thanks you the help :smile:.

 

[HallsofIvy]

All math teachers are tired- that's no excuse!

 

[stapel]

Hi Stapel,

you are right I'm trying to simplify...

From the thumbnail you posted, it looks as though you are missing some very important background information, like maybe your school placed you in the wrong class (so you skipped the one you'd needed right below this one). Do you have a math-help room or something at your school, so you could get some private instruction on stuff like exponents?