Intermediate Algebra: Connecting Concepts through Application

$(x+9y)^{2}$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $\dfrac{(x+9y)^7}{(x+9y)^5} ,$ use the laws of exponents. $\bf{\text{Solution Details:}}$ Using the Quotient Rule of the laws of exponents, which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to \begin{array}{l}\require{cancel} \dfrac{(x+9y)^7}{(x+9y)^5} \\\\= (x+9y)^{7-5} \\\\= (x+9y)^{2} .\end{array}