What is the value of (625)^(1/4)?

What is the value of (625)^(1/4)?

• A. 2
• B. 3
• C. 4
• D. 5

Answer: (D)

Taking a number to the 1/4 power is finding its fourth root. Look for a number that, when raised to the fourth power, gives 625. Recognize that 5^4 equals 625, since 5×5×5×5 = 625. Using the exponent rule (a^b)^c = a^(bc), you get (625)^(1/4) = (5^4)^(1/4) = 5^(4×1/4) = 5. Because even roots pick the nonnegative root, the result is 5. For reference, 2^4 = 16, 3^4 = 81, and 4^4 = 256, none of which equal 625.

Taking a number to the 1/4 power is finding its fourth root. Look for a number that, when raised to the fourth power, gives 625. Recognize that 5^4 equals 625, since 5×5×5×5 = 625. Using the exponent rule (a^b)^c = a^(bc), you get (625)^(1/4) = (5^4)^(1/4) = 5^(4×1/4) = 5. Because even roots pick the nonnegative root, the result is 5. For reference, 2^4 = 16, 3^4 = 81, and 4^4 = 256, none of which equal 625.