Convert to Radical Form (-32)^0.6

${(- 32)}^{0.6}$

Change $0.6$ into a fraction.

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

${(- 32)}^{\frac{10 \cdot 0.6}{10}}$

Multiply $10$ by $0.6$ .

${(- 32)}^{\frac{6}{10}}$

Cancel the common factor of $6$ and $10$ .

Factor $2$ out of $6$ .

${(- 32)}^{\frac{2 (3)}{10}}$

Cancel the common factors.

Factor $2$ out of $10$ .

${(- 32)}^{\frac{2 \cdot 3}{2 \cdot 5}}$

Cancel the common factor.

${(- 32)}^{\frac{2 \cdot 3}{2 \cdot 5}}$

Rewrite the expression.

${(- 32)}^{\frac{3}{5}}$

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

$\sqrt[5]{{(- 32)}^{3}}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt[5]{{(- 32)}^{3}}$

Decimal Form:

$- 8$