Evaluate (1/81)^(-3/4)

Problem

(1/81)(−3/4)

Solution

1. Apply the negative exponent rule by taking the reciprocal of the base to change the exponent to positive.

(1/81)(−3/4)=81

2. Rewrite the base as a power of a prime number, noting that 81=3

81=(3)3/4

3. Apply the power of a power rule by multiplying the exponents.

(3)3/4=3(4⋅3/4)

4. Simplify the exponent by canceling the common factor of 4.

3(4⋅3/4)=3

5. Evaluate the final power by calculating 3 cubed.

3=27

Final Answer

(1/81)(−3/4)=27

Want more problems? Check here!