16^(-1/2)
(27)^(1/3) - with questions that have two brackets, only the first number has brackets on paper.
(27)^(-1/3)
(-27)^(1/3)
(-27)^(-1/3)
(-2)^(-3)

2. Originally Posted by princess_anna57

16^(-1/2)
(27)^(1/3) - with questions that have two brackets, only the first number has brackets on paper.
(27)^(-1/3)
(-27)^(1/3)
(-27)^(-1/3)
(-2)^(-3)
$\displaystyle x^{m/n} = \sqrt[n]{x^m}$

$\displaystyle x^{-n} = \frac1{x^n}$

3. ## Thanks!

I got the first three, but I'm not sure about the last ones. What difference does it make if x is a negative? does it mean that it's undefined/does not exist?

4. Originally Posted by princess_anna57
I got the first three, but I'm not sure about the last ones. What difference does it make if x is a negative? does it mean that it's undefined/does not exist?
Well, if you try to take the square root (or any even root) of a negative number, you will not get a real answer (because the square of any real number is nonnegative). However, you can take cube roots of a negative number, and in fact you can take the $\displaystyle n^{\rm th}$ root of a negative number as long as $\displaystyle n$ is odd.

Thus, $\displaystyle \sqrt[3]{-27} = -3$, for example, because $\displaystyle (-3)^3 = (-3)(-3)(-3) = -27$.