Calculus Examples

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

Step 1

Convert expressions with fractional exponents to radicals.

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Step 1.1

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[3]{{(x^{2} - 3 x)}^{1}}$

Step 1.2

Anything raised to $1$ is the base itself.

$\sqrt[3]{x^{2} - 3 x}$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3