Final answer:
To find the cube root of 512 and the reciprocal of 0.4, raise 512 to the power of 1/3 and divide 1 by 0.4. Finally, divide the cube root by the reciprocal to get the answer in the form n : 1.
Step-by-step explanation:
To find the cube root of 512, we can use the fact that the fourth root is the same as raising it to the power of 1/4. The cube root can be found by raising 512 to the power of 1/3:
512^(1/3) = 8
To find the reciprocal of 0.4, we can divide 1 by 0.4:
1 / 0.4 = 2.5
Finally, we can express the answer in the form n : 1 by dividing the cube root of 512 by the reciprocal of 0.4:
8 / 2.5 = 3.2 : 1