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Hi!
Square roots where the things under the root are multiplied (for example ) can be split up into
.
That's what I'm going to do in this case. I'm going to split into
Now, the cube root of 125 is 5, because 5 * 5 * 5 = 125, and that is the definition of a cube root. (What multiplied 3 times by itself is equal to what's under the root)
Now to look at what the cube root of is.
A cube root can be rewritten as , same as a square root can be rewritten to
.
So if you take the cube root of x^12, you can change it to:
If you have a case like this, then you can multiply the two powers (in this case 12 and 1/3) to simplify it. 12 * 1/3 = 4, so you get x^4.
Now putting the two together, you get:
5 as your answer.
Hope this helped!