How do you simplify?

Question

12x^-3/y^4 times (y^-2x^2)^-1/15x^-2?

Answer 1

This is certainly easier to see if we "draw" them as fractions with horizontal lines. It isn't easy to "draw" that on the computer, but let me try. Here is your original expression:

12 x^-3 .. (y^-2 x^2)^-1
--------- x ----------------
.. y^4 .......... 15 x^-2

Since x^-a is the same as 1/x^a, you can switch any negative exponents from top to bottom or bottom to top and make them all positive exponents.

So you'd have:

...12 ........ 15 x^2
--------- x ------------
x^3 y^4 ....y^-2 x^2

Oops, now you have a y^-2 that can move also:

...12 .......15 x^2 y^2
--------- x ------------
x^3 y^4 ....... x^2

You can cancel a few terms, the x^2 terms cancel, and the y^2 cancels partially with the y^4. Remember to subtract the exponents when cancelling:

...12 .......15
--------- x ----
x^3 y^2 ... 1

Now you can multiply across for your final answer:

. 180
---------
x^3 y^2

Other rules that are important:
x^a * x^b = x^(a + b)

So if you had x^5 * x^4, you could make it x^9 (add exponents).

x^a / x^b = x^(a - b)

So if you had y^7 / y^5, you could make it y^2 (subtract exponents).

x^1 = x

This is pretty obvious, but just wanted to include it for completeness.

Anyway, as stated before, the simplified expression is:

. 180
---------
x^3 y^2

Answer 2

12x^-3/y^4 times (y^-2x^2)^-1/15x^-2?
so i'm going to rewrite this without negative exponents, which means x^-2 = 1/(x^2)
12/(x^3 y^4) * (15 y^2 x^2 / x^2)
cancel out x^2
12/(x^3 y^4) * (15 y^2)
cancel out y^2
12 / (x^3 y^2) * 15
so finally answer is 180 / (x^3 y^2) or 180 x^-3 y^-2 if i didn't make any mistakes.

Answer 3

Combine like terms. Do the ^ marks mean 'squared'?

Answer 4

uhh holy ****. i hope you're in college or something! yikes. i can't even begin to remember that all but i wanna say something about if its multiplied it can be put together or something.....sorry. writeing this for you to read this was kind of a waste of your time......