# Simplify each of the following expressions. Be sure that your answer has no negative or fractional exponents. a*(1/81)^(-1/4)b*x^(-2)y^(-4)c*(2x)^(-2)(16x^2y)^(1/2)

Simplify each of the following expressions. Be sure that your answer has no negative or fractional exponents. $a\cdot \left(\frac{1}{81}{\right)}^{-\frac{1}{4}}b\cdot {x}^{-2}{y}^{-4}c\cdot \left(2x{\right)}^{-2}\left(16{x}^{2y}{\right)}^{\frac{1}{2}}$

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a)
${\frac{1}{81}}^{-\frac{1}{4}}$
$=\left(\frac{1}{3}{\right)}^{-\frac{1}{4}}$
$=\left(\frac{1}{3}\right)$ (product of power property)
$\left(\frac{1}{3}{\right)}^{-1}=3$
b)
${x}^{2}{y}^{-}4$
$={x}^{-2}\cdot {y}^{-4}$
$\frac{1}{{x}^{2}}\cdot \frac{1}{{y}^{4}}$ (negative power property)
c)
$\left(2x{\right)}^{-2}\left(16{x}^{2y}{\right)}^{\frac{1}{2}}$
$={2}^{-2}\cdot {x}^{-2}\cdot {2}^{\frac{4}{2}}\cdot {x}^{\frac{2}{2}}\cdot {y}^{\frac{1}{2}}$ (product of power property)
$={2}^{\left(2-2\right)}\cdot {x}^{\left(1-2\right)}\cdot {y}^{\frac{1}{2}}$
$=1\cdot {x}^{-1}\cdot y\left(\frac{1}{2}\right)$