Final answer:
To simplify (x^(1/2))(x^(1/4)), we add the exponents together because the bases are the same, resulting in x^(3/4).
Step-by-step explanation:
The student is asking about simplifying an expression with rational exponents. To simplify (x1/2)(x1/4), we use the law of multiplying exponents with the same base, which states that we should add exponents together in this case. Therefore, the result is:
x1/2 + 1/4 = x2/4 + 1/4 = x3/4.This simplification relies on understanding that a fractional exponent denotes a root of the base number. That is, x1/2 is the square root of x, and x1/4 is the fourth root of x.