Final answer:
The expression ((3x^(1/4))^3)/(x^(1/12)) simplifies to 27x^(2/3) by applying the rules of exponents to multiply and subtract exponents respectively.
Step-by-step explanation:
To simplify the given mathematical expression ((3x^(1/4))^3)/(x^(1/12)), use the rule of exponents which states that (a^(m))^n equals a^(m*n). This rule lets us multiply the exponents together when an exponent is raised to another exponent. So, (3x^(1/4))^3 simplifies to 3^3 * x^(3/4), which equals 27x^(3/4).
Next, divide this by x^(1/12). To divide terms with the same base, subtract the exponents. So, 27x^(3/4) / x^(1/12) simplifies to 27x^((3/4) - (1/12)). Subtracting the exponents gives us 27x^(2/3).
So, the simplified expression is 27x^(2/3).
Learn more about simplifying exponents