Final answer:
Since 1/64 is in the denominator and we want to get rid of the fraction, we can rewrite it as 1/2^6.Raising 1/2^6 to the power of 1/6 gives us (1/2^6)^(1/6) = 1/2^(6*(1/6)) = 1/2^1 = 1/2.
Therefore, ((1)/(64))¹/⁶ is equal to 1/2.
Step-by-step explanation:
To evaluate ((1)/(64))¹/⁶, we are looking for the sixth root of ⅛. The sixth root of a number is the number that, when multiplied by itself six times, gives the original number. Since 64 is 2 raised to the sixth power (2^6), the sixth root of 64 is 2. Therefore, the sixth root of ⅛ is 1/2, because 1 remains unchanged when taking a root, and the sixth root of 64 is 2. So, the expression simplifies to ½ or 0.5 in decimal form.