Final answer:
To factor out x^3 from the square root, multiply the exponent 3 by 1/2 to get x^(3/2), which is the square root of x^3 and corresponds to option a) x^(3/2).
Step-by-step explanation:
To factor out x^3 from the square root, you need to apply the rules of exponents, specifically when dealing with roots and powers combined. Since taking a square root is equivalent to raising to the power of 1/2, and you want to take the square root of x^3, you would multiply the exponents together. This means you multiply 3 (from x^3) by 1/2 (from the square root), which is 3/2. Therefore, the factored form of x^3 after taking a square root is x^(3/2), which matches option a) x^(3/2).