To determine which statement accurately describes the expression [tex]\(\left|x^3\right| + 5\)[/tex], let's break down the expression and compare it to each option provided.
### Breakdown of the Expression:
1. Cube a number [tex]\(x\)[/tex]: Mathematically, this is written as [tex]\(x^3\)[/tex].
2. Take the absolute value of the cube: This is represented as [tex]\(|x^3|\)[/tex].
3. Add 5 to the result of the absolute value: So, we get [tex]\(|x^3| + 5\)[/tex].
Now, let's evaluate each option:
Option A: "the absolute value of three times a number added to 5"
- This would suggest we are taking the absolute value of three times a number [tex]\(3x\)[/tex] and adding 5 to it.
- Expression: [tex]\(|3x| + 5\)[/tex]
- This does not match our original expression [tex]\(|x^3| + 5\)[/tex].
Option B: "the sum of the absolute value of three times a number and 5"
- Similar to option A, it implies taking the absolute value of [tex]\(3x\)[/tex] and adding 5.
- Expression: [tex]\(|3x| + 5\)[/tex]
- Again, this does not match the original expression, as it involves [tex]\(3x\)[/tex] rather than [tex]\(x^3\)[/tex].
Option C: "the cube of the sum of a number and 5"
- This implies we first add [tex]\(x\)[/tex] and 5, then cube the result.
- Expression: [tex]\((x + 5)^3\)[/tex]
- This is different from our original expression because the operations and their order are not the same.
Option D: "5 more than the absolute value of the cube of a number"
- This describes taking the cube of [tex]\(x\)[/tex], applying the absolute value, and then adding 5.
- Expression: [tex]\(|x^3| + 5\)[/tex]
- This exactly matches our original expression.
### Conclusion:
The statement that correctly describes the expression [tex]\(\left|x^3\right|+5\)[/tex] is:
D. 5 more than the absolute value of the cube of a number
Thus, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
