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img of Evaluate the expression, if possible.  \((-64)^{1/6}\)...

Question: Evaluate the expression, if possible. \((-64)^{1/6}\) Select the correct choice below and fill…

Evaluate the expression, if possible.

\((-64)^{1/6}\)

Select the correct choice below and fill in any answer boxes in your choice.

A. \((-64)^{1/6} = \boxed{\quad}\) (Type an integer or a simplified fraction.)

B. The answer is not a real number.

Solution

To evaluate the expression \((-64)^{1/6}\), we first consider whether this expression has a real number solution. The expression is asking for the sixth root of \(-64\). Since 64 is a perfect power of 2 (\(64 = 2^6\)), we have: \[ (-64)^{1/6} = (-(2^6))^{1/6} \] The sixth root of a negative number is not a real number, because any real number raised to an even power results in a positive number, not a negative one. Thus, the answer is: B. The answer is not a real number.

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