SOLUTION: solve 3^0x^-3y over 2x^-1y^-2

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Question 1180869: solve 3^0x^-3y over 2x^-1y^-2
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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=%281%2A%281%2Fx%5E3%29%2Ay%29%2F%282%281%2Fx%29%2A%281%2Fy%5E2%29%29

=%28y%2Fx%5E3%29%2F%282%2F%28x%2Ay%5E2%29%29


=%28y%2Ax%2Ay%5E2%29%2F%282x%5E3%29......simplify

=%28cross%28x%29%2Ay%5E3%29%2F%282x%5Ecross%283%29%5E2%29

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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Of course it is valid to simplify the expression by replacing each factor with a negative exponent with a reciprocal -- e.g., x^(-2) gets replaced with 1/x^2 and y^(-1) gets replaced with 1/y.

But that creates fractions within fractions, which are awkward to work with.

I think it is far easier to use a simple rule, when simplifying an expression like this, that says each factor with a negative exponent gets moved to the other part of the fraction with a positive exponent.



Of course the 3^0 is 1. Then the x^(-3) in the numerator becomes x^3 in the denominator; the x^(-1) in the denominator becomes x in the numerator, and the y^-2 becomes y^2 in the numerator:

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Then simplify from there if, as in this case, there are still like factors in the numerator and denominator.

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