Final answer:
The expression x^(3/7)/x^(1/4) is simplified by subtracting the exponents, resulting in x^(5/28) after finding a common denominator for the exponents.
Step-by-step explanation:
To simplify the expression x^(3/7)/x^(1/4), we apply the rule for division of exponentials which states that we should subtract the exponents when dividing two exponential terms with the same base. In this case, we subtract 1/4 from 3/7. To find a common denominator for the exponents, we would use 28 because it is the least common multiple of 4 and 7.
Converting both exponents to have the denominator 28, we get:
x^3/7 = x^12/28
x^1/4 = x^7/28
Now we subtract the exponents:
x^12/28 / x^7/28 = x^(12/28 - 7/28) which simplifies to x^5/28. This is the simplified form of the original expression.