Final answer:
To simplify the expression (5³)^(1/2), we multiply the exponents and rewrite it as 5^(3/2). This means taking the square root of 5 cubed, which is 5^(3/2). The simplified expression is 5².5.
Step-by-step explanation:
To simplify the expression (5³)^(1/2), we can apply the law of exponents which states that when a power is raised to another power, we multiply the exponents. In this case, 5³ is being raised to the power of 1/2. To simplify, we multiply 3 by 1/2, which gives us 3/2. So, (5³)^(1/2) can be rewritten as 5^(3/2).
Now, when we have a fractional exponent, it indicates the root of the base. In this case, the exponent 3/2 represents the square root of 5 cubed. Taking the square root of 5 cubed is the same as raising 5 to the power of 3/2, which gives us the answer 5^(3/2).
Therefore, the simplified expression is option c. 5².5.