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

Problem

(1/625)3/4

Solution

1. Rewrite the base as a power of a prime number by identifying that 625=5

(1/625)3/4=(1/5)3/4

2. Apply the negative exponent rule 1/(an)=a(−n) to move the base to the numerator.

(5(−4))3/4

3. Use the power of a power rule (am)n=a(m⋅n) to multiply the exponents.

5(−4⋅3/4)

4. Simplify the exponent by canceling the 4 in the numerator and denominator.

5(−3)

5. Evaluate the negative exponent by taking the reciprocal and calculating 5=125

1/5=1/125

Final Answer

(1/625)3/4=1/125

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