Algebra Examples

${(- 32)}^{0.4}$

Step 1

Change $0.4$ into a fraction.

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Step 1.1

Multiply by $\frac{10}{10}$ to remove the decimal.

${(- 32)}^{\frac{10 \cdot 0.4}{10}}$

Step 1.2

Multiply $10$ by $0.4$ .

${(- 32)}^{\frac{4}{10}}$

Step 1.3

Cancel the common factor of $4$ and $10$ .

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Step 1.3.1

Factor $2$ out of $4$ .

${(- 32)}^{\frac{2 (2)}{10}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $10$ .

${(- 32)}^{\frac{2 \cdot 2}{2 \cdot 5}}$

Step 1.3.2.2

Cancel the common factor.

${(- 32)}^{\frac{2 \cdot 2}{2 \cdot 5}}$

Step 1.3.2.3

Rewrite the expression.

${(- 32)}^{\frac{2}{5}}$

Step 2

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

$\sqrt[5]{{(- 32)}^{2}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt[5]{{(- 32)}^{2}}$

Decimal Form:

$4$