## Intermediate Algebra (12th Edition)

$\dfrac{4x^{7}}{9y^{10}}$
Use the laws of exponents to simplify the given expression, $(3x^{-2}y^3)^{-2}(4x^3y^{-4}) .$ Using the law of exponents which states that $(a^xb^y)^z=a^{xz}b^{yz},$ the expression above simplifies to \begin{array}{l}\require{cancel} (3^{-2}x^{-2(-2)}y^{3(-2)})(4x^3y^{-4}) \\\\= (3^{-2}x^{4}y^{-6})(4x^3y^{-4}) .\end{array} Using the law of exponents which states that $a^x\cdot a^y=a^{x+y},$ the expression above simplifies to \begin{array}{l}\require{cancel} (3)^{-2}(4)x^{4+3}y^{-6+(-4)} \\\\= (3)^{-2}(4)x^{7}y^{-10} .\end{array} Using the law of exponents which states that $a^{-x}=\dfrac{1}{a^x}$ or $\dfrac{1}{a^{-x}}=a^x$ the expression above simplifies to \begin{array}{l}\require{cancel} \dfrac{(4)x^{7}}{(3)^{2}y^{10}} \\\\= \dfrac{4x^{7}}{9y^{10}} .\end{array}