Question

If k 1/3 = integer and k 1/2= integer, which is a possible value for k?

A) -64 B) -8
C) -1
D) 64

Answer 1

To find a possible value for k in k(1/3) = integer and k(1/2) = integer, we need to look for integers that, when raised to the given powers, result in an integer. The possible values for k are -8, -1, and 64.

Step-by-step explanation:

To find a possible value for k, we need to solve the equations k1/3 = integer and k1/2 = integer. Since both exponents are fractions, we need to find integers that can be raised to these powers to give us an integer result. Let's look at the answer choices:

1. -64
2. -8
3. -1
4. 64

Starting with the first choice, if we raise -64 to the power of 1/3, we get -4. Since this is not an integer, we can eliminate this option. Next, if we raise -8 to the power of 1/3, we get -2. This is an integer, so it could be a possible value for k. However, to be thorough, let's check the other options as well.

Raising -1 to the power of 1/3 gives us -1, which is an integer. Finally, raising 64 to the power of 1/3 gives us 4, which is also an integer. Therefore, the possible values for k are -8, -1, and 64.