What is \sqrt[10]{(-32)^6} ?

The solution to \sqrt[10]{(-32)^6} is -8

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simplify \sqrt[10]{(-32)^6}

simplify

- 8

Solution steps

Apply radical rule:

= ((- 32)^{6})^{\frac{1}{10}}

Apply exponent rule:

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

= (- 32)^{6 \cdot \frac{1}{10}}

6 \cdot \frac{1}{10} = \frac{3}{5}

= (- 32)^{\frac{3}{5}}

Apply exponent rule:

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

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

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

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

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

3 2^{\frac{3}{5}} = 8

= - 1 \cdot 8

Multiply the numbers:

1 \cdot 8 = 8

= - 8

5.8216 \cdot 1 0^{(- 6)} \cdot 164.8915

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- 3200 e^{- 16} \cdot \frac{5}{59}

99 \cdot e^{- 0.25 \cdot 30}