Evaluate 81^(-1/2)

Problem

81(−1/2)

Solution

1. Apply the negative exponent rule which states that a(−n)=1/(an)

81(−1/2)=1/(81(1/2))

2. Rewrite the fractional exponent as a square root using the rule a(1/2)=√(,a)

1/(81(1/2))=1/√(,81)

3. Evaluate the square root of 81.

√(,81)=9

4. Simplify the fraction to find the final value.

1/9

Final Answer

81(−1/2)=1/9

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