Final answer:
To express 25^(3/2) in simplest radical form, we rewrite it as (5^2)^(3/2), multiply the exponents to get 5^3, and convert this to radical form as sqrt(125), which simplifies to 5 * sqrt(5).
Step-by-step explanation:
To express 25(3/2) in its simplest radical form, we can break down the expression by understanding how exponents and radicals relate to each other. In general, an exponent written as a fraction indicates a root, where the denominator of the fraction is the root and the numerator is the power to which the radical is raised.
Let's apply this to 25(3/2):
- First, recognize that 25 is a perfect square since 25 = 52.
- Now, we rewrite the expression as (52)(3/2).
- Next, using the rule that (xa)b = x(a*b), we multiply the exponents: 2 * (3/2) = 3.
- Thus, the expression simplifies to 53, which is equal to 5 * 5 * 5.
- In radical form, this is sqrt(53) or, more conventionally, sqrt(125).
In conclusion, 25(3/2) in its simplest radical form is sqrt(125) or, if we break it down further, it's the cube of 5 inside the square root, which is 5 * sqrt(5).