If F(X) is defined as 3X^(2/3), what is the value of F(-8)?

If F(X) is defined as 3X^(2/3), what is the value of F(-8)?

• A. 8
• B. 10
• C. 12
• D. 14

Answer: (C)

To find the value of F(-8) for the function F(X) = 3X^(2/3), we first need to substitute -8 for X in the function. This gives us: F(-8) = 3 * (-8)^(2/3). Now, let's break down the expression (-8)^(2/3): 1. The power of 2/3 can be interpreted as first taking the cube root and then squaring the result. So, we can rewrite (-8)^(2/3) as [(-8)^(1/3)]^2. 2. The cube root of -8 is -2, since (-2) * (-2) * (-2) = -8. 3. Now, squaring -2 gives us (-2)^2 = 4. Putting it all together, we have: F(-8) = 3 * 4 = 12. Therefore, the value of F(-8) is correctly calculated as 12. This matches the value given in the choice labeled "C."

To find the value of F(-8) for the function F(X) = 3X^(2/3), we first need to substitute -8 for X in the function. This gives us:

F(-8) = 3 * (-8)^(2/3).

Now, let's break down the expression (-8)^(2/3):

1. The power of 2/3 can be interpreted as first taking the cube root and then squaring the result. So, we can rewrite (-8)^(2/3) as [(-8)^(1/3)]^2.

2. The cube root of -8 is -2, since (-2) * (-2) * (-2) = -8.

3. Now, squaring -2 gives us (-2)^2 = 4.

Putting it all together, we have:

F(-8) = 3 * 4 = 12.

Therefore, the value of F(-8) is correctly calculated as 12. This matches the value given in the choice labeled "C."