Question

Which number in the monomial 125x^18y^3z^25 needs to be changed to make it a perfect cube

Answer 1

Hi,

You just have to change z^25 to z^24 or z^27.

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

Answer 2

The required number in teh polynomial needs to be changes to make it a perfect cube is
`z^(25)` .

Explanation:

Given : Expression
`125x^(18)y^3z^(25)`

To find : Which number in the monomial expression needs to be changed to make it a perfect cube?

Solution :

Expression
`125x^(18)y^3z^(25)`

Using property,

`(x^a)^b=x^(ab)` and
`(xy)^a=x^ay^a`

Now we distribute each term into a power cube.

`125=5^3`

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

`y^(3)=y^(3\cdot 1)`

`z^(25)=z^(3\cdot 8+1)`

We have seen that

`z^(25)` is not making a multiple of 3 so to make it a perfect cube we have to change it into
`z^(24)=Z^(3\cdot 8)`

Now, Making a perfect cube with the change

`125x^(18)y^3z^(25)`

`=5^3x^(3\cdot 6)y^(3\cdot 1)z^(3\cdot 8)`

`=(5)^3(x^(6))^3(y)^(3)(z^8)^3`

`=(5x^6yz^8)^3`

Therefore, The required number in teh polynomial needs to be changes to make it a perfect cube is
`z^(25)` .