Evaluate 81^(-3/4)

Problem

81^(−3/4)

Solution

1. Rewrite the expression using the property of negative exponents, a^(−n)=1/(a^n)

1/(81^(3/4))

2. Apply the definition of rational exponents, a^(m/n)=(√(n,a))^m

1/((√(4,81))^3)

3. Evaluate the fourth root of 81 by identifying that 3^4=81

√(4,81)=3

4. Substitute the root back into the expression.

1/3^3

5. Calculate the final value by cubing the denominator.

3^3=27

Final Answer

81^(−3/4)=1/27

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