F(x) is the function that determines the absolute value of the cube of the input.

1.) Evaluate: F(5)
2.) Evaluate: F(-7)
3.) Determine: F(5)⋅F(-7)

f(x) = |x^3|

f(5) = |5^3| = |125| = 125
work the others in the same way, recalling that
|x| = x if x >= 0
|x| = -x if x < 0
the cube of a negative value is also negative (but that doesn't really matter here, since we're taking its absolute value)

1.) Ah, evaluating F(5), huh? Well, let's see. The absolute value of the cube of 5... that's the cube of 5 without any negativity business. So, the absolute value of 5 cubed is... 125! Voila!

2.) Now, onto evaluating F(-7). Brace yourself! We need the absolute value of the cube of -7. The cube of -7 is -343, but remember, we need the absolute value, so it becomes 343.

3.) Lastly, determining F(5)⋅F(-7)... Okay, multiplying 125 (from F(5)) by 343 (F(-7))... Finding some humor in math is no easy task, but the result is 42,875. Yep, that's it!

To evaluate the function F(x) which determines the absolute value of the cube of the input, follow these steps:

1.) Evaluate F(5):
- Start with the input value of 5.
- Cube 5: 5^3 = 125.
- Take the absolute value of 125: |125| = 125.
- Therefore, F(5) = 125.

2.) Evaluate F(-7):
- Start with the input value of -7.
- Cube -7: (-7)^3 = -343.
- Take the absolute value of -343: |-343| = 343.
- Therefore, F(-7) = 343.

3.) Determine F(5)⋅F(-7):
- Multiply the values of F(5) and F(-7): 125 * 343 = 42,875.
- The product of F(5)⋅F(-7) is 42,875.

To evaluate the given function F(x) = |x^3|, we need to follow these steps:

1.) Evaluate F(5):
To find F(5), substitute 5 into the function:
F(5) = |5^3|
= |125|
= 125
Therefore, F(5) = 125.

2.) Evaluate F(-7):
To find F(-7), substitute -7 into the function:
F(-7) = |-7^3|
= |-343|
= 343
So, F(-7) = 343.

3.) Determine F(5)⋅F(-7):
To calculate F(5)⋅F(-7), multiply the values of F(5) and F(-7):
F(5)⋅F(-7) = 125 × 343
≈ 429,375
Therefore, F(5)⋅F(-7) ≈ 429,375.