I am overthinking this but (−4)(−52) is not a valid equation, am I correct? Working through the problem gives me 1−452 which then works out to 1−45 which leaves a negative number in the square root, which is not valid.

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Joy Compton · Accepted Answer

It is perfectly valid, the result is simply not a Real Number, it is what is called an Imaginary Number (or a Complex Number in the case in which you had a Real Numbered component as well), which you may not be familiar with.  The result you gave simplifies down to −132i, where i is called the Imaginary Unit, and is equal to −1

gekraamdbk · Accepted Answer

The square root of a negative number is a complex number (−4)−52=1−45=1(2i)5=−132i. If this sounds like complete gibberish to you, google &quot;imaginary numbers&quot; and read up on it.

I am overthinking this but (-4)^{(-5/2)} is not a valid

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