SOLUTION: Simplify the expression and express your answer using positive exponents only. (3^2xy^-1)^-2(6x^-4y^3)(9x^3y^-2)^3/(3x^-3y^-4)^2

Question 1118977: Simplify the expression and express your answer using positive exponents only.
(3^2xy^-1)^-2(6x^-4y^3)(9x^3y^-2)^3/(3x^-3y^-4)^2
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

There are all kinds of different sequences of steps you could take to simplify an expression like this. For someone just learning about problems like this, I would probably suggest the following:
(1) simplify the "3^2"
(2) wherever an expression in parentheses is raised to a power, "distribute" the exponent to the factors inside the parentheses
(3) simplify the coefficient (the numerical part of the answer)
(4) wherever that leaves you with a negative exponent, move that factor to the denominator if it is in the numerator, or move it to the numerator if it is in the denominator
(5) combine exponents on each variable in the numerator and denominator
(6) cancel factors where needed to end up with an expression containing each variable only once and with a positive exponent

Again, there are numerous variations on the sequence of steps you can take to perform the simplification.

If you are thoroughly familiar with the process of simplifying expressions like these, you can accomplish all but the last step in a single step:

in the numerator...
.. (3^2)^-2) gives 9^-2, which gives me a 9^2 in the denominator
.. x^-2 gives me an x^2 in the denominator
.. (y^-1)^-2 gives me a y^2 in the numerator
.. the 6 stays in the numerator
.. (x^-4) gives me an x^4 in the denominator
.. the y^3 stays in the numerator
.. the 9^3 stays in the numerator
.. the (x^3)^3 gives me an x^9 in the numerator
.. the (y^-2)^3 gives y^-6, which gives me a y^6 in the denominator

in the denominator...
.. 3^2 gives me 9, which stays in the denominator
..(x^-3)^2 gives me x^-6, which gives me an x^6 in the numerator
..(y^-4)^2 gives me y^-8, which gives me a y^8 in the numerator

And now write all the factors in their proper places...

Simplify the coefficient and combine exponents in the numerator and denominator...

and simplify...

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