Simplify x^2y^-4*(x^3y^2)

Problem

x2*y(−4)*(x3*y2)

Solution

1. Group like bases by rearranging the terms so that the x variables and y variables are adjacent.

x2⋅x3⋅y(−4)⋅y2

2. Apply the product rule for exponents, which states am⋅an=a(m+n) to the x terms.

x(2+3)⋅y(−4)⋅y2

x5⋅y(−4)⋅y2

3. Apply the product rule to the y terms by adding their exponents.

x5⋅y(−4+2)

x5⋅y(−2)

4. Rewrite with positive exponents using the rule a(−n)=1/(an) to move y(−2) to the denominator.

(x5)/(y2)

Final Answer

x2*y(−4)*(x3*y2)=(x5)/(y2)

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