Question

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

Answer 1

z^25 needs to be z^24 to make a perfect cube

if z^24 then

125x^18y^3z^24 = 5^3 (x^6)^3 y^3 (z^8)^3

Answer 2

`z^(25)` has to be changed.

Explanation:

The given monomial is
`125x^(18)y^(3)z^(25)`.

If we see the separate terms of the monomial then we find that each term can be written in perfect cube form except z.

125 = 5³

`x^(18)=(x^(6))^(3)`

y³ is in cube form

`z^(25)` is the only term which can be written in the perfect cube form if it is
`z^(24)=(z^(8))^(3)` or
`z^(27)=(z^(9))^(3)`

So the answer is
`z^(25)`