Question

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)

Exponents and radicals
ANSWERED
asked 2021-03-04

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

Answers (1)

2021-03-05

a)
\(\frac{1}{81}^{-\frac{1}{4}}\)
\(=(\frac{1}{3})^{-\frac{1}{4}}\)
\(=(\frac{1}{3})\) (product of power property)
\((\frac{1}{3})^{-1}=3\)
b)
\(x^2 y^-4\)
\(=x^{-2}\cdot y^{-4}\)
\(\frac{1}{x^{2}}\cdot\frac{1}{y^{4}}\) (negative power property)
c)
\((2x)^{-2}(16x^{2y})^{\frac{1}{2}}\)
\(=2^{-2}\cdot x^{-2}\cdot2^{\frac{4}{2}}\cdot x^{\frac{2}{2}}\cdot y^{\frac{1}{2}}\) (product of power property)
\(=2^{(2-2)}\cdot x^{(1-2)}\cdot y^{\frac{1}{2}}\)
\(=1\cdot x^{-1}\cdot y(\frac{1}{2})\)

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