Final answer:
To simplify the expression (x^(1/3))/(x^(-1/2)x^(1/4)), you can subtract the exponents of the exponential expressions with the same base. The simplified result is x^(7/12).
Step-by-step explanation:
To simplify the expression (x1/3)/(x-1/2x1/4), we can use the property of exponents which states that dividing two exponential expressions with the same base is equivalent to subtracting the exponents.
First, we simplify the expression in the numerator by subtracting the exponents: x1/3 divided by x-1/2 is equal to x1/3 - (-1/2).
Next, we simplify the expression in the denominator: x1/4.
Now, we combine the simplified numerator and denominator: (x1/3 - (-1/2))/(x1/4).
To simplify further, we can simplify the exponent expression by finding a common denominator: (x2/6 + 3/6)/(x3/12).
Finally, we can simplify the expression by subtracting the exponents: x5/6 - 3/12, which simplifies to x7/12.