Evaluate (1/625)^(-3/4)

Problem

(1/625)(−3/4)

Solution

1. Apply the negative exponent rule by taking the reciprocal of the base to change the sign of the exponent.

(1/625)(−3/4)=625

2. Rewrite the base as a power of a prime number, noting that 625=5

625=(5)3/4

3. Apply the power of a power rule by multiplying the exponents.

(5)3/4=5(4⋅3/4)

4. Simplify the exponent by canceling the common factor of 4.

5(4⋅3/4)=5

5. Calculate the final value by cubing the base.

5=125

Final Answer

(1/625)(−3/4)=125

Want more problems? Check here!