y=x^((1)/(2))*x^((2)/(3))

Identify base and exponents: Identify the base and the exponents in the expression. We have y = x^(1/2) * x^(2/3), where x is the base, 1/2 and 2/3 are the exponents.Apply multiplication rule: Apply the rule for multiplying powers with the same base. When multiplying powers with the same base, we add the exponents. So, y = x^(1/2 + 2/3).Find common denominator: Find a common denominator to add the fractions. The common denominator for 2 and 3 is 6. So, we convert the fractions: 1/2 = 3/6 and 2/3 = 4/6.Add converted exponents: Add the converted exponents. Now we add the exponents: 3/6 + 4/6 = 7/6. So, y = x^(7/6).Write final simplified expression: Write the final simplified expression. The simplified form of the expression is y = x^(7/6).

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$y=x^{\frac{1}{2}} \cdot x^{\frac{2}{3}}$

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Algebra 1

Multiplication with rational exponents

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

Identify base and exponents: Identify the base and the exponents in the expression. $\newline$ We have $y = x^{\frac{1}{2}} \times x^{\frac{2}{3}}$ , where $x$ is the base, $\frac{1}{2}$ and $\frac{2}{3}$ are the exponents.
Apply multiplication rule: Apply the rule for multiplying powers with the same base. $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ So, $y = x^{\frac{1}{2} + \frac{2}{3}}$ .
Find common denominator: Find a common denominator to add the fractions. $\newline$ The common denominator for $2$ and $3$ is $6$ . $\newline$ So, we convert the fractions: $\frac{1}{2} = \frac{3}{6}$ and $\frac{2}{3} = \frac{4}{6}.$
Add converted exponents: Add the converted exponents. $\newline$ Now we add the exponents: $\frac{3}{6} + \frac{4}{6} = \frac{7}{6}$ . $\newline$ So, $y = x^{\frac{7}{6}}$ .
Write final simplified expression: Write the final simplified expression. $\newline$ The simplified form of the expression is $y = x^{\frac{7}{6}}$ .