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Popular >

simplify \sqrt[7]{(-6)^6}

Solution

simplify

Solution

6^{\frac{6}{7}}

+1

Decimal Notation

4.64501 \dots

Solution steps

Apply radical rule:

= ((- 6)^{6})^{\frac{1}{7}}

Apply exponent rule:

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

= (- 6)^{6 \cdot \frac{1}{7}}

6 \cdot \frac{1}{7} = \frac{6}{7}

= (- 6)^{\frac{6}{7}}

Apply exponent rule:

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

(- 6)^{\frac{6}{7}} = (- 1)^{\frac{6}{7}} \cdot 6^{\frac{6}{7}}

= (- 1)^{\frac{6}{7}} \cdot 6^{\frac{6}{7}}

(- 1)^{\frac{6}{7}} = 1

= 1 \cdot 6^{\frac{6}{7}}

Multiply:

1 \cdot 6^{\frac{6}{7}} = 6^{\frac{6}{7}}

= 6^{\frac{6}{7}}

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Frequently Asked Questions (FAQ)

What is \sqrt[7]{(-6)^6} ?
The solution to \sqrt[7]{(-6)^6} is 6^{6/7}