Evaluate 9^(-3/2)

Problem

9(−3/2)

Solution

1. Apply the negative exponent rule by rewriting the expression as a reciprocal with a positive exponent.

9(−3/2)=1/(9(3/2))

2. Interpret the rational exponent as a combination of a power and a root, specifically the square root of the base raised to the third power.

1/(9(3/2))=1/((√(,9))3)

3. Evaluate the square root of the base.

√(,9)=3

4. Substitute the root back into the expression and calculate the cube.

1/3=1/27

Final Answer

9(−3/2)=1/27

Want more problems? Check here!