What is \sqrt[5]{(-3)^2} ?

The solution to \sqrt[5]{(-3)^2} is 3^{2/5}

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simplify \sqrt[5]{(-3)^2}

simplify

3^{\frac{2}{5}}

Decimal Notation

1.55184 \dots

Solution steps

Apply radical rule:

= ((- 3)^{2})^{\frac{1}{5}}

Apply exponent rule:

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

= (- 3)^{2 \cdot \frac{1}{5}}

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

= (- 3)^{\frac{2}{5}}

Apply exponent rule:

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

(- 3)^{\frac{2}{5}} = (- 1)^{\frac{2}{5}} \cdot 3^{\frac{2}{5}}

= (- 1)^{\frac{2}{5}} \cdot 3^{\frac{2}{5}}

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

= 1 \cdot 3^{\frac{2}{5}}

Multiply:

1 \cdot 3^{\frac{2}{5}} = 3^{\frac{2}{5}}

= 3^{\frac{2}{5}}

(2 \cdot 3.14 \cdot 580000)^{2} \cdot 2.8 \cdot 1 0^{- 9}

(- 0.5)^{(- 0.5)}

- 9.72 e^{- 0.00006}

(x - 2) e^{- x^{2}}

1.8 \cdot 1 0^{- 6} \cdot \frac{500}{0.001}