Questions: Evaluate the following.
(a) (-256)^(1/4) =
Transcript text: Evaluate the following.
(a) $(-256)^{\frac{1}{4}}=$ $\square$
Solution
Solution Steps
Step 1: Evaluate the Fourth Root
To find (−256)41, we recognize that −256 is a negative number. The fourth root of a negative number is not a real number, but it can be expressed in terms of complex numbers.
Step 2: Express in Complex Form
Using the properties of complex numbers, we can express the fourth root of −256 as:
(−256)41=2.8284+2.8284j
This indicates that the result has both a real part and an imaginary part.
Final Answer
The fourth root of −256 is given by:
2.8284+2.8284j