Intermediate Algebra (12th Edition)

$\dfrac{16}{x^{6}y^{16}}$
Use the laws of exponents to simplify the given expression, $(-2x^4y^{-3})^0(-4x^{-3}y^{-8})^2 .$ Using the law of exponents which states that $a^0=1,$ the expression above simplifies to \begin{array}{l}\require{cancel} (1)(-4x^{-3}y^{-8})^2 \\\\= (-4x^{-3}y^{-8})^2 .\end{array} 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} (-4)^2x^{-3(2)}y^{-8(2)} \\\\= 16x^{-6}y^{-16} .\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{16}{x^{6}y^{16}} .\end{array}