To find all real fourth roots of -81, you can use the following steps:
1. Start with the number -81.
2. Take the fourth root of -81:
(-81)^(1/4)
3. Calculate the fourth root:
(-81)^(1/4) = -3
So, the real fourth root of -81 is -3. Since we're looking for all real fourth roots, keep in mind that there are two more complex fourth roots (due to the properties of complex numbers):
4. The other three fourth roots can be found by rotating the complex numbers 90 degrees in a counter-clockwise direction in the complex plane. These roots are:
-3i
3
3i
Therefore, the four real fourth roots of -81 are -3, -3i, 3, and 3i.