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Question

# Simplify. Suppose that all variables represent nonzero integers.$\dfrac{25 x^{a+b} y^{b-a}}{-5 x^{a-b} y^{b+a}}$

Solution

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Using the laws of exponents and order of operations, the expression $\dfrac{25x^{a+b}y^{b-a}}{-5x^{a-b}y^{b+a}}$ simplifies to

\begin{align*} & -5x^{a+b-(a-b)}y^{b-a-(b+a)} \\\\&= -5x^{a+b-a+b}y^{b-a-b-a} \\\\&= -5x^{2b}y^{-2a} \\\\&= \dfrac{-5x^{2b}}{y^{2a}} .\end{align*}

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