Final answer:
To simplify the expression y^(3/2) ⋅x^(-1/2), apply the properties of exponents. Rewrite x^(-1/2) as 1/x^(1/2) and simplify the expression to (y^3/x^(1/2))^(1/2).
Step-by-step explanation:
To simplify the expression y^(3/2) ⋅x^(-1/2), we can apply the properties of exponents. The property states that for any real numbers a and b, (a^m)^n = a^(m*n) and a^m ⋅ a^n = a^(m+n). Applying this property, we have y^(3/2) ⋅ x^(-1/2) = (y^3 ⋅ x^(-1/2))^(1/2). Now, we can rewrite x^(-1/2) as 1/x^(1/2). Therefore, the expression simplifies to (y^3/x^(1/2))^(1/2).