I need help with solving expressions with exponents

(a 1/2 b )1/2 (ab 1/2)

What are the exponents.

To show exponents online -- 5^3 = 5 cubed

This is how the problem is shown in math book

To solve the expression (a^(1/2) * b)^(1/2) * (ab^(1/2)), we can follow the order of operations and simplify step by step.

Step 1: Simplify the first part of the expression:
(a^(1/2) * b)^(1/2)

To simplify the first part, you can rewrite it as the square root of the product of a^(1/2) and b:
√(a^(1/2) * b)

Now, let's simplify the individual factors inside the square root:
√(a^(1/2) * b) = √(√a * b)

Using the rule of exponents, when you have a power to a power, you multiply the exponents, so we have:
√(√a * b) = √(a^(1/4) * b)

Step 2: Simplify the second part of the expression:
(ab^(1/2))

Since there are no operations inside the parentheses here, we don't need to perform any further simplification.

Step 3: Combine the simplified parts:
√(a^(1/4) * b) * (ab^(1/2))

Now, we can multiply the two parts together:
√(a^(1/4) * b) * (ab^(1/2)) = √(a^(1/4) * b) * ab^(1/2)

To simplify the expression further, we can rewrite it as a single square root:
√(a^(1/4) * b) * ab^(1/2) = √(a^(1/4) * b * a * b^(1/2))

Using the rule of exponents, when multiplying variables with the same base, you add the exponents. Applying this rule, we get:
√(a^(1/4) * b * a * b^(1/2)) = √(a^(5/4) * b^(3/2))

Therefore, the simplified expression is √(a^(5/4) * b^(3/2)).