Determine how many times you must use a number as a term in an equation to equal another number. For example, consider the problem: ^n√81 = 3. This problem is saying that you can multiply the number 3 times itself a certain number of times to equal 81. Multiplying 3 x 3 = 9. Multiplying 3 times itself twice -- 3 x 3 x 3 -- you get 27. But if you multiply 3 times itself 3 times -- 3 x 3 x 3 x 3, you get 81. Therefore the nth root in this problem equals 4 because you used the term 3 four times in the equation.
Divide the nth root into the exponent under the radical sign if applicable. For example, ^n√x^m = x^m/n. A numerical example of this would be ^2√2^4 would equal 2^4/2. This can be simplified to 2^2, which equals 4.
Separate terms within multiplication problems containing nth roots as follows:
^n√xy = ^n√x * ^n√y. A numerical example is ^3√16 = ^3√8 * ^3√2. This can be simplified to 2^3√2.
Separate terms within division problems containing nth roots as follows: ^n√x/y = ^n√x / ^n√y. An example of a numerical version is ^3√1/8 = ^3√1 / ^3√8, which can be simplified to ^3√1/2.