Final answer:
The original expression (9a²b^(-5/2))^(1/2) simplifies to 3ab^(-5/4) by raising each part inside the brackets to the power of 1/2.
Step-by-step explanation:
To simplify the given expression (9a²b^(-5/2))^(1/2), the process begins by applying the power of 1/2 to each component inside the parentheses, as indicated. Initially, the square root of 9 yields the value 3. Next, the exponent of a² transforms into a by employing the property that 2*(1/2) equals 1, simplifying a² to a^1, which is just a. Lastly, the exponent of b^(-5/2) is simplified by multiplying it by 1/2, resulting in b^(-5/4).
In conclusion, the simplified expression is 3ab^(-5/4). This concise form is achieved by taking the square root of 9, leaving a's exponent as 1, and transforming the exponent of b^(-5/2) into b^(-5/4). This represents a more compact and manageable version of the original expression, showcasing the power of exponent rules in simplifying mathematical expressions.
Learn more about Simplifying exponential expressions