Evaluate 81^(3/4)

Problem

81(3/4)

Solution

1. Rewrite the expression using the property of rational exponents a(m/n)=(√(n,a))m

81(3/4)=(√(4,81))3

2. Evaluate the fourth root of 81 by identifying that 3⋅3⋅3⋅3=81

√(4,81)=3

3. Substitute the result back into the expression.

3

4. Calculate the final value by raising 3 to the power of 3

3⋅3⋅3=27

Final Answer

81(3/4)=27

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