Select the expression that is equivalent to (1)/((2x)^(-(1)/(3))) (1)/(root(3)(2x)) root(3)(2x) sqrt((2x)^(3)) (1)/(sqrt((2x)^(3)))

Understand Expression: Understand the given expression. We have the expression (1)/((2x)^(-(1)/(3))). This is a fraction with a negative exponent in the denominator.Apply Negative Exponent Rule: Apply the negative exponent rule. The negative exponent rule states that a^(-n) = 1/(a^n). We can apply this rule to move the term with the negative exponent from the denominator to the numerator. (1)/((2x)^(-(1)/(3))) = (2x)^(1/3)Recognize Exponent Meaning: Recognize the meaning of the exponent (1/3). The exponent (1/3) is equivalent to the cube root. Therefore, (2x)^(1/3) is the same as the cube root of 2x. (2x)^(1/3) = root(3)(2x)Compare with Options: Compare the result with the given options. The expression we have found, root(3)(2x), matches one of the given options.

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Select the expression that is equivalent to
(1)/((2x)^(-(1)/(3)))

(1)/(root(3)(2x))

root(3)(2x)

sqrt((2x)^(3))

(1)/(sqrt((2x)^(3)))

Select the expression that is equivalent to $\frac{1}{(2 x)^{-\frac{1}{3}}}$ $\newline$ $\frac{1}{\sqrt[3]{2 x}}$ $\newline$ $\sqrt[3]{2 x}$ $\newline$ $\sqrt{(2 x)^{3}}$ $\newline$ $\frac{1}{\sqrt{(2 x)^{3}}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the expression that is equivalent to

\frac{1}{(2 x)^{-\frac{1}{3}}}

\newline

\frac{1}{\sqrt[3]{2 x}}

\newline

\sqrt[3]{2 x}

\newline

\sqrt{(2 x)^{3}}

\newline

\frac{1}{\sqrt{(2 x)^{3}}}

Understand Expression: Understand the given expression. $\newline$ We have the expression $\frac{1}{(2x)^{-\frac{1}{3}}}$ . This is a fraction with a negative exponent in the denominator.
Apply Negative Exponent Rule: Apply the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-n} = \frac{1}{a^n}$ . We can apply this rule to move the term with the negative exponent from the denominator to the numerator. $\newline$ $\frac{1}{(2x)^{-\frac{1}{3}}} = (2x)^{\frac{1}{3}}$
Recognize Exponent Meaning: Recognize the meaning of the exponent $(1/3)$ . $\newline$ The exponent $(1/3)$ is equivalent to the cube root. Therefore, $(2x)^{(1/3)}$ is the same as the cube root of $2x$ . $\newline$ $(2x)^{(1/3)} = \sqrt[3]{2x}$
Compare with Options: Compare the result with the given options. $\newline$ The expression we have found, $\sqrt[3]{2x}$ , matches one of the given options.