rational exponent on a negative.

[monjinho]

In my math book there is a question: -25^3/2 and (-27)^4/3.
I would think it is impossible to take roots of a negative but my math book apparently says that the answer is -125 and 81.
Can you help me understand this?

[stapel_eliz]

In my math book there is a question: -25^3/2 and (-27)^4/3.
I would think it is impossible to take roots of a negative but my math book apparently says that the answer is -125 and 81.
Can you help me understand this?

Had the first expression been "(-25)^3/2", you'd have been correct. But since the "minus" sign is not included within the expression on which the power has been placed (being instead out in front), taking the square root is legitimate.

For the second expression, you're taking the cube root, so the negative doesn't matter (even if you hadn't been applying an even power first).