Last Updated on May 4, 2023
What is the value of ((.000064)^⅓)^½)…
Solution:
Let’s review the notation first. When an exponent is a fraction, that exponent indicates taking a root. So if we have, for example, 27^1/3, the 1/3 instructs us to take the cube root of 27, which is 3. Similarly, if the exponent were 1/2, such as in 25^1/2, the 1/2 instructs us to take the square root of 25, which is 5.
To solve this question, we can refer to two rules:
1) If a decimal with a finite number of decimal places is a perfect cube, its cube root will have exactly one-third of the number of decimal places. Thus, a perfect cube decimal must have a number of decimal places that is a multiple of 3.
2) If a decimal with a finite number of decimal places is a perfect square, its square root will have exactly half of the number of decimal places. Thus, a perfect square decimal must have an even number of decimal places.
Let’s look first at (0.000064)^1/3. The 1/3 instructs us to take the cube root of 0.000064. By rule number 1, the cube root of 0.000064 = 0.04. We were able obtain this value because 0.000064 has 6 DECIMAL PLACES and because the cube root of 64 is 4.
The problem now looks like this: (0.04)^1/2. The ½ instructs us to find the square root of 0.04. By rule number 2, the square root of 0.04 = 0.2. We were able to obtain this value because 0.04 has 2 DECIMAL PLACES and the square root of 4 is 2.
Answer E.
