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f(x)=2x^((1)/(3))

$7$ . $f(x)=2 x^{\frac{1}{3}}$

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Evaluate integers raised to positive rational exponents

Full solution

Q.

7

.

f(x)=2 x^{\frac{1}{3}}

Identify Function Components: Identify the function and its components. $\newline$ The function given is $f(x) = 2x^{(1/3)}$ . $\newline$ Here, the base is $x$ , and the exponent is $1/3$ , which indicates the cube root of $x$ . $\newline$ The coefficient $2$ is multiplied by the cube root of $x$ .
Recognize Cube Root Exponent: Recognize that the exponent $\frac{1}{3}$ represents the cube root. $\newline$ The expression $x^{\frac{1}{3}}$ is equivalent to the cube root of $x$ , which is written as $\sqrt[3]{x}$ . $\newline$ Therefore, $f(x) = 2x^{\frac{1}{3}}$ can be rewritten as $f(x) = 2\sqrt[3]{x}$ .
Check for Simplifications: Check for any possible simplifications. $\newline$ Since there are no further simplifications that can be made to the expression $2\sqrt[3]{x}$ , this is the simplified form of the function.

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