Question

Which number in the monomial 125x18y3z25 needs to be changed to make it a perfect cube? 3 18 25 125

Answer 1

25

Explanation:

Answer 2

Answer: 25

Reason:

The exponent 25 is not a multiple of 3. If it was something like 24, then we would have a perfect cube as shown below

`w = 125x^(18)y^3z^(24)\\\\w = 5^(1*3)x^(6*3)y^(1*3)z^(8*3)\\\\w=(5^1x^6y^1z^8)^3\\\\w = (5x^(6)yz^(8))^3\\\\`

When going from step 2 to step 3, I used the rule that
`(abcd)^e = a^eb^ec^ed^e`. Basically the exponent e gets applied to each factor inside.