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(x^((8)/(3)))/(x*x^((1)/(2)))

$\frac{x^{\frac{8}{3}}}{x \cdot x^{\frac{1}{2}}}$

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Multiplication with rational exponents

Full solution

Q.

\frac{x^{\frac{8}{3}}}{x \cdot x^{\frac{1}{2}}}

Combine Bases in Denominator: Step $1$ : Combine the bases in the denominator. $\newline$ Reasoning: Since $x$ and $x^{1/2}$ are multiplied together, we add their exponents. $\newline$ Calculation: $x \times x^{1/2} = x^{1 + 1/2} = x^{3/2}.$
Divide Terms by Subtracting Exponents: Step $2$ : Divide the terms by subtracting the exponents. $\newline$ Reasoning: To divide powers with the same base, subtract the exponents of the denominator from the numerator. $\newline$ Calculation: $\frac{x^{\frac{8}{3}}}{x^{\frac{3}{2}}} = x^{\left(\frac{8}{3} - \frac{3}{2}\right)}$ .
Convert Exponents to Common Denominator: Step $3$ : Convert the exponents to a common denominator and subtract. $\newline$ Reasoning: To subtract the fractions, convert $(\frac{3}{2})$ to a fraction with a denominator of $3$ . $\newline$ Calculation: $(\frac{3}{2}) = (\frac{9}{6})$ , so $(\frac{8}{3}) - (\frac{9}{6}) = (\frac{16}{6}) - (\frac{9}{6}) = (\frac{7}{6})$ .

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