Final answer:
64x^9 can be expressed as the cube of the monomial 4x^3, since (4x^3)^3 equals 64x^9.
Step-by-step explanation:
When we wish to express 64x^9 as the cube of a monomial, we are looking for a monomial whose cube equals 64x^9. The process of cubing an exponential involves cubing the numerical coefficient and multiplying the exponent by 3. Therefore, to find the monomial that we can cube to get 64x^9, we need to consider the cube root of 64, which is 4, and divide the exponent by 3, which gives us 3 (since 9 divided by 3 is 3).
Thus, the monomial we are looking for is 4x^3. To verify, we cube this monomial: (4x^3)^3 = 4^3 * x^(3*3) = 64x^9, which is our original expression. Therefore, 64x^9 can be expressed as the cube of the monomial 4x^3.