Final answer:
The expression 9x to the power of 3/2 is equivalent to the square root of 9x all cubed, written as √(9x)^3 or (√9x)^3.
Step-by-step explanation:
The expression 9x3/2 can be rewritten as a radical expression by interpreting the exponent as a fraction. In rational exponent notation, the numerator indicates the power to which the base is raised and the denominator indicates the root that is being taken. Therefore, an expression like Am/n is equivalent to the nth root of A raised to the mth power or √Am.
In the case of 9x3/2, the 2 in the denominator tells us we are dealing with a square root, and the 3 in the numerator tells us we are cubing the quantity inside the root. Hence, the equivalent radical expression is the square root of 9x cubed, which can be written as √(9x)3 or alternatively as (√9x)3 since the square root and the cubing are performed on the entire expression 9x.