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

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

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

simplify

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

Decimal Notation

2.92401 \dots

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

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

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

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

Apply exponent rule:

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

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

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

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

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

Multiply:

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

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

\frac{( - 4 π ^{2} ) ^{2}}{5.2 7 ^{2}} \cdot 0.6 3^{2}

1.9958 e^{- (3.075 3^{2})}

1.5 \cdot 1 0^{- 8}

s^{2} (1 + 0.06 s)^{2} (1 + 0.22 s)^{2}

0.002 \cdot e^{- 0.122542}