What is \sqrt[5]{(-6)^4} ?

The solution to \sqrt[5]{(-6)^4} is 6^{4/5}

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simplify \sqrt[5]{(-6)^4}

simplify

6^{\frac{4}{5}}

Decimal Notation

4.19296 \dots

Solution steps

Apply radical rule:

= ((- 6)^{4})^{\frac{1}{5}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (- 6)^{4 \cdot \frac{1}{5}}

4 \cdot \frac{1}{5} = \frac{4}{5}

= (- 6)^{\frac{4}{5}}

Apply exponent rule:

(- a)^{\frac{m}{n}} = (- 1)^{\frac{m}{n}} (a)^{\frac{m}{n}}

(- 6)^{\frac{4}{5}} = (- 1)^{\frac{4}{5}} \cdot 6^{\frac{4}{5}}

= (- 1)^{\frac{4}{5}} \cdot 6^{\frac{4}{5}}

(- 1)^{\frac{4}{5}} = 1

= 1 \cdot 6^{\frac{4}{5}}

Multiply:

1 \cdot 6^{\frac{4}{5}} = 6^{\frac{4}{5}}

= 6^{\frac{4}{5}}

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