Evaluate 25^(-3/2)

Problem

25(−3/2)

Solution

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

25(−3/2)=1/(25(3/2))

2. Interpret the rational exponent using the rule a(m/n)=(√(n,a))m where the denominator 2 represents a square root.

1/(25(3/2))=1/((√(,25))3)

3. Evaluate the square root of the base number.

√(,25)=5

4. Substitute the result back into the expression.

1/5

5. Calculate the power by multiplying the base by itself three times.

5=125

Final Answer

25(−3/2)=1/125

Want more problems? Check here!