Questions: (a) -81^(1/4)= (b) (-1024)^(1/5)=

(a) -81^(1/4)= (b) (-1024)^(1/5)=
Transcript text: (a) $-81^{\frac{1}{4}}=$ (b) $(-1024)^{\frac{1}{5}}=$
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Solution

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Solution Steps

Step 1: Calculate \( -81^{\frac{1}{4}} \)

To find \( -81^{\frac{1}{4}} \), we compute the fourth root of -81. The result is a complex number given by: \[ -81^{\frac{1}{4}} = 2.1213 + 2.1213j \]

Step 2: Calculate \( (-1024)^{\frac{1}{5}} \)

Next, we calculate \( (-1024)^{\frac{1}{5}} \), which is the fifth root of -1024. The result is also a complex number: \[ (-1024)^{\frac{1}{5}} = 3.2361 + 2.3511j \]

Final Answer

The results for the calculations are: \[ -81^{\frac{1}{4}} = \boxed{2.1213 + 2.1213j} \] \[ (-1024)^{\frac{1}{5}} = \boxed{3.2361 + 2.3511j} \]

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