Questions: Simplify the following expression. Express your answer using the same notation as the original expression. x^(4/3) y^(1/2) / x^(-5/3) y

Simplify the following expression. Express your answer using the same notation as the original expression. x^(4/3) y^(1/2) / x^(-5/3) y
Transcript text: Simplify the following expression. Express your answer using the same notation as the original expression. \[ \frac{x^{\frac{4}{3}} y^{\frac{1}{2}}}{x^{\frac{-5}{3}} y} \]
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Solution

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Solution Steps

Step 1: Simplify the exponents of \( x \)

\[ \frac{x^{\frac{4}{3}}}{x^{\frac{-5}{3}}} = x^{\frac{4}{3} - \left(-\frac{5}{3}\right)} = x^{\frac{4}{3} + \frac{5}{3}} = x^{\frac{9}{3}} = x^3 \]

Step 2: Simplify the exponents of \( y \)

\[ \frac{y^{\frac{1}{2}}}{y} = y^{\frac{1}{2} - 1} = y^{-\frac{1}{2}} \]

Step 3: Combine the simplified terms

\[ x^3 \cdot y^{-\frac{1}{2}} = \frac{x^3}{y^{\frac{1}{2}}} \]

Final Answer

\(\boxed{\frac{x^3}{y^{\frac{1}{2}}}}\)

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