Compute 16^(3/4).

Compute 16^(3/4).

• A. 4
• B. 8
• C. 2
• D. 16

Answer: (B)

Fractional exponents let you treat the exponent 3/4 as first taking the fourth root and then cubing. Write 16 as 2^4, so 16^(3/4) = (2^4)^(3/4) = 2^(4*(3/4)) = 2^3 = 8. Equivalently, take the fourth root of 16 to get 2, then cube it to get 8.

Fractional exponents let you treat the exponent 3/4 as first taking the fourth root and then cubing. Write 16 as 2^4, so 16^(3/4) = (2^4)^(3/4) = 2^(4*(3/4)) = 2^3 = 8. Equivalently, take the fourth root of 16 to get 2, then cube it to get 8.