Pregunta
What is \( \frac{x^{\frac{2}{3}} y}{x^{\frac{2}{3}} y^{\frac{1}{3}}} \) in \( [ \) simplest exponential form?
Ask by Harris Campbell. in the United States
Mar 11,2025
Solución de inteligencia artificial de Upstudy
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The expression simplifies to \( \sqrt[3]{y^{2}} \).
Solución
Calculate or simplify the expression \( \frac{x^{2/3}y}{x^{2/3}y^{1/3}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{x^{\frac{2}{3}}y}{x^{\frac{2}{3}}y^{\frac{1}{3}}}\)
- step1: Reduce the fraction:
\(\frac{y}{y^{\frac{1}{3}}}\)
- step2: Reduce the fraction:
\(\frac{y^{1-\frac{1}{3}}}{1}\)
- step3: Simplify:
\(y^{1-\frac{1}{3}}\)
- step4: Divide the terms:
\(y^{\frac{2}{3}}\)
- step5: Simplify:
\(\sqrt[3]{y^{2}}\)
The expression \( \frac{x^{\frac{2}{3}} y}{x^{\frac{2}{3}} y^{\frac{1}{3}}} \) in simplest exponential form is \( \sqrt[3]{y^{2}} \).
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Simplifique esta solución Extra Insights
To simplify \( \frac{x^{\frac{2}{3}} y}{x^{\frac{2}{3}} y^{\frac{1}{3}}} \), we can use the properties of exponents. First, divide the \( x \) terms: \[ \frac{x^{\frac{2}{3}}}{x^{\frac{2}{3}}} = x^{\frac{2}{3} - \frac{2}{3}} = x^{0} = 1 \] Next, divide the \( y \) terms: \[ \frac{y}{y^{\frac{1}{3}}} = y^{1 - \frac{1}{3}} = y^{\frac{2}{3}} \] Now, combining both parts, we get: \[ \frac{x^{\frac{2}{3}} y}{x^{\frac{2}{3}} y^{\frac{1}{3}}} = 1 \cdot y^{\frac{2}{3}} = y^{\frac{2}{3}} \] Thus, the expression simplifies to: \[ y^{\frac{2}{3}} \] So, the final answer in simplest exponential form is \( y^{\frac{2}{3}} \).
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