Solved: "Simplify each of the following expressions. Be sure..."

High School
Algebra
Algebra I
Exponents and radicals

Maiclubk

Answered question

2021-03-04

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

Answer & Explanation

Cristiano Sears

Skilled2021-03-05Added 96 answers

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)
$(2 x)^{- 2} (16 x^{2 y})^{\frac{1}{2}}$
$= 2^{- 2} \cdot x^{- 2} \cdot 2^{\frac{4}{2}} \cdot x^{\frac{2}{2}} \cdot y^{\frac{1}{2}}$ (product of power property)
$= 2^{(2 - 2)} \cdot x^{(1 - 2)} \cdot y^{\frac{1}{2}}$
$= 1 \cdot x^{- 1} \cdot y (\frac{1}{2})$

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