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“Area of Triangle in Parabola”: In the future can I always "factor" a cube root to simplify it?

Question

In the future can I always "factor" a cube root to simplify it? The following equation featured in one of the practice questions:  k^3 = 1/64 with the final answer being = 1/4. I understand that 1^3 = 1 and 4^3 = 64 but I was initially stumped when I first had to simplify k^3 = 1/64.

Answer

We are solving for k. So to solve when we get to k^3 = 1/64, we need to take the cube root of both sides.

Since here k^3 = 1/64, we take the cube root of 1/64 and get k = 1/4. Since (1/4)^3 = 1^3/4^3 = 1/64

If we have k^n = b, we take the nth root of b.

If k^n = 1/b, then we would have 1 divide by the nth root of b.

Link

https://gre.magoosh.com/questions/2192

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