What is \sqrt[-4]{(-81)^3} ?

The solution to \sqrt[-4]{(-81)^3} is 1/(27(-1)^{3/4)}

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simplify \sqrt[-4]{(-81)^3}

simplify

\frac{1}{27 ( - 1 ) ^{\frac{3}{4}}}

Solution steps

Apply radical rule:

= ((- 81)^{3})^{\frac{1}{- 4}}

Apply exponent rule:

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

= (- 81)^{3 \cdot \frac{1}{- 4}}

3 \cdot \frac{1}{- 4} = - \frac{3}{4}

= (- 81)^{- \frac{3}{4}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( - 81 ) ^{\frac{3}{4}}}

Apply exponent rule:

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

(- 81)^{\frac{3}{4}} = (- 1)^{\frac{3}{4}} \cdot 8 1^{\frac{3}{4}}

= \frac{1}{( - 1 ) ^{\frac{3}{4}} \cdot 8 1 ^{\frac{3}{4}}}

8 1^{\frac{3}{4}} = 27

= \frac{1}{27 ( - 1 ) ^{\frac{3}{4}}}

ln (3) (e^{- 2 x})

e^{- 1.063382}

(2.5 \cdot 50 \cdot 2 \cdot π \cdot 43 \cdot 1 0^{6})^{- 1}

((- 22)^{2} - 8) e^{- 22}

e^{\frac{- x}{2}} \cdot e^{\frac{- x}{2}}

What is \sqrt[-4]{(-81)^3} ?
The solution to \sqrt[-4]{(-81)^3} is 1/(27(-1)^{3/4)}