Final answer:
To simplify (a^2b^4c)^3, you apply the exponent rule (x^a)^b = x^(a*b), resulting in a^6b^12c^3 after multiplying the exponents for each variable.
Step-by-step explanation:
To simplify the expression (a^2b^4c)^3, we need to apply the rule of exponents which states that when you raise a power to a power, you multiply the exponents. To clarify, for any base x and exponents a and b, the rule is (x^a)^b = x^(a*b).
In this case, we have:
a raised to the 2nd power and then cubed, which gives us a^(2*3) = a^6,
b raised to the 4th power and then cubed, which results in b^(4*3) = b^12, and
c raised to the 1st power (since no exponent is visible, it's implied to be 1) and then cubed, giving c^(1*3) = c^3.
Combining all of these, the simplified expression is a^6b^12c^3.