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Chapter 0: Problem 103

Simplify the expressions. $$ \frac{x^{1 / 2} y^{2}}{x^{-1 / 2} y} $$

Short Answer

Expert verified
The simplified expression is \(y\).

Step by step solution

01

Rewrite the expression using properties of exponents for multiplication

We can rewrite the expression as follows: $$ \frac{x^{1 / 2} y^{2}}{x^{-1 / 2} y} = x^{1/2}\cdot x^{-1/2}\cdot y^{2}\cdot y^{-1} $$
02

Simplify the x term

To simplify the x term, subtract the exponents: $$ x^{(1/2) + (-1/2)} $$ Because the exponents have the same denominator, we can subtract the numerators directly: $$ x^{((1 - 1)/2)} = x^{0} $$ Remember that any number raised to the power of 0 is equal to 1: $$ x^{0} = 1 $$
03

Simplify the y term

To simplify the y term, subtract the exponents: $$ y^{(2) + (-1)} = y^{(1)} $$
04

Combine the simplified terms

We will now combine the simplified x and y terms to obtain the final simplified expression: $$ 1 \cdot y^{1} = y $$ So, the simplified expression is: $$ y $$

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Most popular questions from this chapter

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(3-\frac{4+7}{8}\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(\frac{3-1}{8+6}\)

Find all possible real solutions of each equation \(2 x^{6}-x^{4}-2 x^{2}+1=0\)

Giving the answer as \(a\) whole number or a fraction in lowest terms. $$ 20 /(3 * 4)-1 $$

\((3 x+1)\left(2 x^{2}-x+1\right)\)
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