Question 1180869
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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.<br>
But that creates fractions within fractions, which are awkward to work with.<br>
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.<br>
{{{((3^0)(x^(-3))(y))/((2)(x^(-1))(y^(-2)))}}}<br>
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:<br>
{{{((1)(x)(y^2)(y))/((2)(x^3))}}}<br>
Then simplify from there if, as in this case, there are still like factors in the numerator and denominator.<br>
{{{((y^3))/((2)(x^2))}}}<br>