SOLUTION: Simplify using the laws of exponents: (3x^3y^2/2z^5)^3(-4z^8/9x^4y^3)^3 If a solution was shown, that'd be much appreciated! Still trying to figure this out.

Question 1092034: Simplify using the laws of exponents:
(3x^3y^2/2z^5)^3(-4z^8/9x^4y^3)^3
If a solution was shown, that'd be much appreciated! Still trying to figure this out.
Answer by greenestamps(13208) (Show Source): You can put this solution on YOUR website!

There are many different paths to the final simplified form. Different students will have preferences for different steps to do first....

The given expression is

I put the coefficients 3, 2, -4, and 9 in parentheses to emphasize that they, as well as the variables and their exponents, need to be raised to the prescribed powers. Many beginning students fail to realize that.

Since there are two complex fractions being mutliplied together, we can combine all the factors in the numerators and denominators of the two fractions, raised to the appropriate powers, in a single fraction.

For the numerical part the simplified form, we have
and

so the numerical part of the simplified form is -8/27.

Then simplifying the exponents on the variables is easy, using basic rules.

x: 9 factors in the numerator, 12 in the denominator --> 3 factors left in the denominator

y: 6 factors in the numerator, 9 in the denominator --> 3 factors left in the denominator

z: 24 factors in the numerator, 15 in the denominator --> 9 factors left in the numerator

And the final simplified form is

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