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 $(-256)^{\frac{1}{4}}$, 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: \[ (-256)^{\frac{1}{4}} = 2.8284 + 2.8284j \] This indicates that the result has both a real part and an imaginary part.

Final Answer

The fourth root of $-256$ is given by: \[ \boxed{2.8284 + 2.8284j} \]

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