(a^3b^3)9ab)^-2 simplified is ab Right?

Question

Thank you for all that help!..
Im just unsure of this new stuff we're learning in class.
Thanks!

Shoot, i typed the 9 ^ up there wrong. its supposed to be the (***

Answer 1

Assuming your 9 was a typo, intended to be a parenthesis (they are the same key and I'm constantly mistyping 9...)

(a^3b^3)(ab)^-2

Then this is the same as:
(a^3b^3)/(a²b²).

You would cancel a²b² leaving only a and b in the numerator.

Thus your answer of 'ab' is exactly right! Good job!

Answer 2

(9ab(a ^ 3 * b^ 3)) ^ -2
Think of a ^ 3 * b ^ 3 as one unit then evaluate 9ab(a ^ 3 * b^3)
9ab (a^3 * b^3) = 9 (a ^ 4 * b ^ 4) take that answer and raise it to the - 2 power. A formula for this is : z ^ -x = 1 / (z^x). Therefore,
9(a ^ 4 * b ^ 4) ^ -2 = 1 / (9(a^4 b^4)) ^ 2 = 1 / (81 (a ^ (4* 2) b ^ (4* 2))) = 1 / (81 (a^8 b^8))
To check, let a = 2 and b = 3.
9(2)(3) ((2 ^ 3) * (3^3)) ^ -2 = (54 * (8 * 27)) ^ -2 = 1 / (11664 ^ 2) = 1 / 136048896
Now check my answer with the same numbers
1 / 81 (2 ^ 8) (3 ^ 8) == 1 / (81 *256 * 1679616) = 1 / 136048896. It checks.

Answer 3

well the parenthesis don match..
assumin it to be((a^3 b^3)9ab)^-2

it simplifies to 1/(3(ab)^2)

Answer 4

Um, no way. Did you copy this down correctly?

* * * * *

Right, like the next poster says... good detective work on his part.

Answer 5

(a^3b^3)(ab)^-2
= (a^3b^3)(a^-2)(b^-2)
= a^(3-2)b^(3-2)
=a^1b^1
=ab