Final answer:
The cube root of 1/64 is found by identifying a number that, when cubed, equals 1/64. In this case, 1/4 is the number that satisfies this condition, making 1/4 the cube root of 1/64.
Step-by-step explanation:
To find the real cube root of 1/64, let's consider the definition of a cube root. The cube root of a number is the value that, when multiplied by itself three times, gives the original number. For integers, the cube root of a perfect cube (like 64) is an integer. Since 64 is 4 multiplied by itself three times (4 x 4 x 4), the cube root of 64 is 4.
To find the cube root of 1/64, we just need to apply this logic to the fraction. That is, find a number that when multiplied by itself three times results in 1/64. We know that 1/4 multiplied by itself three times (1/4 x 1/4 x 1/4) equates to 1/64. Therefore, the cube root of 1/64 is, indeed, 1/4. The correct answer to the question is: a) Cube root of 1/64 is 1/4.