Question

is 64x^15y^18 a perfect cube?

Answer 1

Would it be easier if we write
\(64x^{15}y^{18}=2^6x^{15}y^{18} \)
noting that all powers are divisible by three.

Answer 2

Yes, so it would be a difference of cubes because they are all divisible by 3?

Answer 3

A perfect cube will have all powers divisible by three, because, for example:
\((5xy^2)^3=5^3x^3y^6\)
the cube of an expression is obtained by multiplying the exponents by three.

Answer 4

Then how do i know if an expression is a difference of cubes?

Answer 5

Question is asking perfect cube where the exponents are all divisible by 3.

Difference of cubes is a different concept, something like:
\(\huge x^3-y^3 = (x-y)(x^2+xy+y^2)\)
and is related to factorization.

Answer 6

ahhhh i think i get it, i was mistaking them to be together. Thank you

Answer 7

You're welcome! :)