Questions: Evaluate the following. (a) (-256)^(1/4) =

Evaluate the following.
(a) (-256)^(1/4) =
Transcript text: Evaluate the following. (a) $(-256)^{\frac{1}{4}}=$ $\square$
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Solution

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Solution Steps

Step 1: Evaluate the Fourth Root

To find (256)14(-256)^{\frac{1}{4}}, we recognize that 256-256 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 256-256 as: (256)14=2.8284+2.8284j (-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 256-256 is given by: 2.8284+2.8284j \boxed{2.8284 + 2.8284j}

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