Hello there,

I'm stuck on two problems that have exponents/radicals. I have the answer to each of them but can't figure out how to get there. I know this may seem a little 'below' what normally goes on here but it's pretty much a lock that any help I get will be right.

The first is this: y^3/4SQRTy (not sure how to write that) It's "y" to the third power over (index of) 4 (radical sign) with a "y" under the radical sign. The answer (back of the book...with NO explaination, gah!) is y with the exponent fraction of 11/4.

The second is x^-2 y^2 over 2 with the whole fraction in ( ) to the -3 power.
The answer is 8x^6 over y^6.

What I'd really like to hear is that the book is wrong.

It would be great to know what this operation is called, then I could look it up. But I don't even know what property (or maybe even properties) should be used. I tried a couple of the "math help" sites but they really don't go into exponent fractions. I had three problems that I couldn't get but got one worked out. These two are killing me.

Thanks for your time.

For the 2nd one, multiply the -3 into the parenthesis:

((x^-2 y^2)/2)^-3 = x^6 y^-6 / (2^-3)

see if you can take it from there.

__________________
www.gravitysimulator.com

You can't have a radical as a denominator. You have to multiply both the numerator and denominator by the sqrt y.

__________________
Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

Try this page: http://www.wtamu.edu/academic/anns/m...ationalize.htm

__________________
Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

The following is from my wife, the math teacher. It took us awhile to puzzle out the first problem, but this seems to provide the correct answer.

ETA: We had some problems attaching the solution (JPEG format). Let me know if you have problems reading it.

Attached Images

answer1.jpg (38.6 KB, 17 views)

Shoot I was thinking 4 times sqrt y.

__________________
Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

That's why I couldn't get the 1st one! I was reading 4*sqrt(y), not y^(1/4). It's too bad this forum doesn't have LaTex.

edit: Tinaa too I see!

__________________
www.gravitysimulator.com

I couldn't get it to work either.

__________________
Insanity: doing the same thing over and over again and expecting different results.
Albert Einstein

I worked the problem several different ways myself before giving up and showing it to my wife. It took her a minute or two to figure it out so I didn't feel totally ignorant. Incidentally, she used MathType to write out the equations which we then converted to jpg for the attachment.

Ha ha! I used to be a math teacher, too, some number of moons ago, and I looked at that first problem, confident that I could solve any high school problem at least, and thought... "Huh?"

The stopwatch was running. So I was a little rusty. It was six seconds later that I recalled that the key to the problem was that the fourth root of y in the denominator was equivalent to y to the one-fourth (in the denominator), which is the same as y to the minus one-fourth in the numerator.

From there, there are a number of ways to "crunch the numbers."

I went from y³/y^1/4 to y^2+3/4 to y^11/4.

__________________
Everyone is entitled to his own opinion, but not his own facts.

My problem was figuring out what the original problem was. Oh, to have a scratch pad capability. Having the answer is what allowed us to figure it out and then on to the solution. Is there a math editor/equation writer available here on BAUT?

More importantly, jra-xp...did any of this help? Next time you log in, hopefully, you'll let us all know.

One must note, however, that the bases of these oddly occurring exponents are the same: y. Otherwise, one cannot simply add or subtract exponents to simplify the expression.

__________________
Everyone is entitled to his own opinion, but not his own facts.

Oh, right. I had to transcribe it onto... a scratch pad.

__________________
Everyone is entitled to his own opinion, but not his own facts.

It helped me as I couldn't understand the first problem at all. Thanks and especially thanks to your wife. Nicely explained.

"(index of) 4" is the correct terminology for a fourth root....

__________________
Everyone is entitled to his own opinion, but not his own facts.

Wow! Thanks guys!

That helped completely!

Great site. Does that mean these are college algebra questions? Which would be cool.



Awsome. Tell Mrs. ABR she's a friggin hero. The write up was what I needed.
3. change 3 over 1 to 12 over 4 by multiplying top and bottom by four.
This is actually in the book, but I didn't make the connection. You have to really know the basic rules to get this stuff to work out right. Once you know the rules its knowing when to do what that matters.

And the second problem,
2. move the x squared from the bottom to the top to make the exponent positive.

I think this is a combination of Property 5 and 6. (also in the book...sheesh)

a^-n = 1 over a^n
a^-1 = 1 over a

I think what those mean is that you can flip the exponent up or down by just changing the sign.

I got all the other questions right, these two were by far the hardest because what you had to do wasn't right out in front.

Thanks again, I'm glad some of you were stumped as well.

Sorry!

I didn't realize that the posts went to the moderator first before being put up. I posted the same thing like 8 times thinking it was busted....

Sorry for that.

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That's weird. This post went up fast. Maybe it's the quotes that make it moderator checked....

Glad to be of help, jra-xp (says the guy who just attached the jpg). I've passed your message along to my wife -- yours, too Veeger. She reminded me that this stuff is what she does for a living!