Evaluate 81^(-1/4)

Problem

81(−1/4)

Solution

1. Apply the negative exponent rule by rewriting the expression as the reciprocal with a positive exponent using the property a(−n)=1/(an)

1/(81(1/4))

2. Interpret the fractional exponent as a radical using the property a(1/n)=√(n,a)

1/√(4,81)

3. Find the fourth root of the base by identifying which number raised to the power of 4 equals 81

3=81

4. Substitute the root into the expression to find the final value.

1/3

Final Answer

81(−1/4)=1/3

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