Write the expression as a single power of x. (x^((4)/(3)))/(x^((2)/(3)))

Identify Given Expression: Identify the given expression and the rule for dividing powers with the same base. The rule is: a^(m)/a^(n) = a^(m-n). Here, we have x^(4/3) / x^(2/3).Apply Division Rule: Subtract the exponents of x using the rule for dividing powers with the same base. (4/3) - (2/3) = (4 - 2)/3 = 2/3. So, x^(4/3) / x^(2/3) = x^(2/3).Check for Errors: Check for any mathematical errors in the previous steps. Subtraction of fractions was done correctly, and the rule for dividing powers with the same base was applied correctly.

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Write the expression as a single power of x.
(x^((4)/(3)))/(x^((2)/(3)))

Write the expression as a single power of $x$ . $\newline$ $\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}}}$

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Q. Write the expression as a single power of

x

\newline

\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}}}

Identify Given Expression: Identify the given expression and the rule for dividing powers with the same base. $\newline$ The rule is: $a^{m}/a^{n} = a^{m-n}$ . $\newline$ Here, we have $x^{\frac{4}{3}} / x^{\frac{2}{3}}$ .
Apply Division Rule: Subtract the exponents of $x$ using the rule for dividing powers with the same base. $\frac{4}{3} - \frac{2}{3} = \frac{4 - 2}{3} = \frac{2}{3}$ . So, $x^{\frac{4}{3}} / x^{\frac{2}{3}} = x^{\frac{2}{3}}$ .
Check for Errors: Check for any mathematical errors in the previous steps. Subtraction of fractions was done correctly, and the rule for dividing powers with the same base was applied correctly.