What is the sign of - a^4/3 when a is less than zero

A positive

B negative

C zero

Answer: B. Negative

Reasoning:

'a' is less than 0, so we write a < 0

Since a 0. Raising a negative to an even exponent will make the result positive. Example: (-2) ^4 = 16

Applying the cube root to some positive number leads to some other positive number.

So far we see that the expression a^ (4/3) is positive

The final result however is negative because the negative out front flips things from positive to negative.

It turns out it doesn't matter if 'a' is positive or negative. As long as 'a' is nonzero, then - a^ (4/3) is negative. If a = 0, then the whole thing is 0.