Which number in the monomial 215x18y3z21 needs to be changed to make it a perfect cube?
3
18
21
215

We need to remember that:
                   xyz = (x)(y)(z)
if x, y and z are perfect cubes, then xyz would also be a perfect cube

Also, 
                 (x^n)^m = x^(mn)
if it is a perfect cube, then it can be factored into the expression (x^n)^3, wherein n is a whole number.

All should be a perfect cube, given

215x^18(y^3)(z^21)

By writing the terms separately, we would see which one is to be changed. 

215 = 5*43, we see this is not a perfect cube, we could changed it to 6^3 or 216

x^18=(x^6)^3

y^3=y^3
z^21=(z^7)^3

The other terms are perfect cubes except for the first one. So the correct answer would be the last option, 215 should be changed.

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