What is the square root of 16 raised to the fourth power?

What is the square root of 16 raised to the fourth power?

• A. 16
• B. 1024
• C. 256
• D. 64

Answer: (C)

Working with radicals and exponents together uses the rule that a power raised to another power multiplies the exponents: (a^(1/2))^n = a^(n/2). Here a is 16 and n is 4. So you can convert the square root to an exponent form: (16^(1/2))^4 = 16^(4/2) = 16^2 = 256. You can also think by evaluating the root first: √16 = 4, then 4^4 = 256. Or use the equivalent path √(16^4) = (16^4)^(1/2) = 16^(4/2) = 16^2 = 256. In every approach, the result is 256.

Working with radicals and exponents together uses the rule that a power raised to another power multiplies the exponents: (a^(1/2))^n = a^(n/2). Here a is 16 and n is 4. So you can convert the square root to an exponent form: (16^(1/2))^4 = 16^(4/2) = 16^2 = 256. You can also think by evaluating the root first: √16 = 4, then 4^4 = 256. Or use the equivalent path √(16^4) = (16^4)^(1/2) = 16^(4/2) = 16^2 = 256. In every approach, the result is 256.