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Popular >

simplify \sqrt[5]{(-7)^2}

Solution

simplify

Solution

7^{\frac{2}{5}}

+1

Decimal Notation

2.17790 \dots

Solution steps

Apply radical rule:

= ((- 7)^{2})^{\frac{1}{5}}

Apply exponent rule:

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

= (- 7)^{2 \cdot \frac{1}{5}}

2 \cdot \frac{1}{5} = \frac{2}{5}

= (- 7)^{\frac{2}{5}}

Apply exponent rule:

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

(- 7)^{\frac{2}{5}} = (- 1)^{\frac{2}{5}} \cdot 7^{\frac{2}{5}}

= (- 1)^{\frac{2}{5}} \cdot 7^{\frac{2}{5}}

(- 1)^{\frac{2}{5}} = 1

= 1 \cdot 7^{\frac{2}{5}}

Multiply:

1 \cdot 7^{\frac{2}{5}} = 7^{\frac{2}{5}}

= 7^{\frac{2}{5}}

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Frequently Asked Questions (FAQ)

What is \sqrt[5]{(-7)^2} ?
The solution to \sqrt[5]{(-7)^2} is 7^{2/5}