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 −8114 -81^{\frac{1}{4}}

To find −8114 -81^{\frac{1}{4}} , we compute the fourth root of -81. The result is a complex number given by: −8114=2.1213+2.1213j -81^{\frac{1}{4}} = 2.1213 + 2.1213j

Step 2: Calculate (−1024)15 (-1024)^{\frac{1}{5}}

Next, we calculate (−1024)15 (-1024)^{\frac{1}{5}} , which is the fifth root of -1024. The result is also a complex number: (−1024)15=3.2361+2.3511j (-1024)^{\frac{1}{5}} = 3.2361 + 2.3511j

Final Answer

The results for the calculations are: −8114=2.1213+2.1213j -81^{\frac{1}{4}} = \boxed{2.1213 + 2.1213j} (−1024)15=3.2361+2.3511j (-1024)^{\frac{1}{5}} = \boxed{3.2361 + 2.3511j}

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