Evaluate 81^(5/4)

Problem

81(5/4)

Solution

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

81(5/4)=(√(4,81))5

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

√(4,81)=3

3. Substitute the root back into the expression.

3

4. Calculate the final value by multiplying 3 by itself five times (3⋅3⋅3⋅3⋅3.

3=243

Final Answer

81(5/4)=243

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