What is (\sqrt[4]{-16})^5 ?

The solution to (\sqrt[4]{-16})^5 is -32\sqrt[4]{-1}

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simplify (\sqrt[4]{-16})^5

simplify

Solution steps

Apply radical rule:

= ((- 16)^{\frac{1}{4}})^{5}

Apply exponent rule:

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

= (- 16)^{\frac{1}{4} \cdot 5}

\frac{1}{4} \cdot 5 = \frac{5}{4}

= (- 16)^{\frac{5}{4}}

Apply exponent rule:

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

(- 16)^{\frac{5}{4}} = (- 1)^{\frac{5}{4}} \cdot 1 6^{\frac{5}{4}}

= (- 1)^{\frac{5}{4}} \cdot 1 6^{\frac{5}{4}}

1 6^{\frac{5}{4}} = 32

Remove parentheses:

(- a) = - a

Multiply the numbers:

1 \cdot 32 = 32

(9.6 x 1 0^{- 1}) (5.2 x 1 0^{2})

55 \cdot x x

((e^{- 3 x}) + (e^{7 x}))^{- 11}

0.5 \cdot 1.0 1^{- 0.167}

(5)^{x}

What is (\sqrt[4]{-16})^5 ?
The solution to (\sqrt[4]{-16})^5 is -32\sqrt[4]{-1}