Evaluate 16^(1/4).

Evaluate 16^(1/4).

• A. 3
• B. 4
• C. sqrt(16)
• D. 2

Answer: (D)

Taking a fractional exponent means finding a root. The expression 16^(1/4) asks for the fourth root of 16. Write 16 as 2^4, then use the power-of-a-power rule: (2^4)^(1/4) = 2^(4*(1/4)) = 2^1 = 2. Another way is to do it step by step with roots: sqrt(sqrt(16)) = sqrt(4) = 2. The other numbers wouldn’t work when raised to the fourth power (3^4 = 81, 4^4 = 256), and taking the square root twice would give 4, which is not the fourth root. So the value is 2.

Taking a fractional exponent means finding a root. The expression 16^(1/4) asks for the fourth root of 16. Write 16 as 2^4, then use the power-of-a-power rule: (2^4)^(1/4) = 2^(4*(1/4)) = 2^1 = 2. Another way is to do it step by step with roots: sqrt(sqrt(16)) = sqrt(4) = 2. The other numbers wouldn’t work when raised to the fourth power (3^4 = 81, 4^4 = 256), and taking the square root twice would give 4, which is not the fourth root. So the value is 2.