High School

Which number in the monomial [tex]215x^{18}y^{3}z^{21}[/tex] needs to be changed to make it a perfect cube?

A. 3
B. 18
C. 21
D. 215

Answer :

remember
xyz=(x)(y)(z)
if x and y and z are all perfect cubes, xyz is also a perfect cube

remmeber
(x^n)^m=x^(mn)
so if it is perfect cube it can be factored into
(x^n)^3, such taht n is a whole number
basiclaly, see if the expoent is divisble by 3

all of them should be perfect cubes

215x^18y^3z^21

split them up to see which ones need changing

215=5*43, not a perfect cube
could be changed to 6^3, which is 216

x^18=(x^6)^3

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

the 215 needs to be changed

Answer: E2020 = 215

Step-by-step explanation: