Question

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

Answer 1

Answer:

The required number in teh polynomial needs to be changes to make it a perfect cube is $z^{25}$ .

Step-by-step 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 $z^{25}$ .

Answer 2

Hi,

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

$125x^{18}y^3z^{24}=(5x^6*y*z^8)^3$