Final answer:
The expression equivalent to (6x^5z)^3/4x^4z^2 is 9x^11z/2, which we get by cubing the components of the numerator and then dividing by the components of the denominator and simplifying.
Step-by-step explanation:
To find the expression equivalent to (6x^5z)^3 divided by 4x^4z^2, we first simplify the numerator by cubing both the coefficient and the variables. Cubing 6 gives us 216, and the exponent rules indicate that when we raise an exponential term to a power, we multiply the exponents. Therefore, the cubed term becomes 216x^15z^3. Then, we divide this by 4x^4z^2.
Dividing the coefficients, we get 216/4, which is 54. For the variables, we subtract the exponents in the denominator from those in the numerator for the same base, leading to x^(15-4) which is x^11 and z^(3-2) which is z. Hence, the equivalent expression is (54x^11z)/(4x^4z^2), which simplifies further to 9x^11z/2 by dividing both the numerator and denominator by 6.