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Which can be used to describe the expression? Check all that apply.

(r -4)3
There are three factors of r -4.
The expression is equal to 1 over 12 factors of r.
Adding the exponents will create an equivalent expression.
Multiplying the exponents will create an equivalent expression.
The expression simplifies to StartFraction 1 Over r Superscript 7 Baseline EndFraction.

1 answer

Let's analyze the expression \((r - 4)^3\) to determine which statements can be used to describe it.

  1. There are three factors of \(r - 4\).
    True. The expression \((r - 4)^3\) represents \((r - 4) \times (r - 4) \times (r - 4)\), so there are indeed three factors of \(r - 4\).

  2. The expression is equal to \(1\) over \(12\) factors of \(r\).
    False. The expression \((r - 4)^3\) does not equate to \(1\) over \(12\) factors of \(r\). This statement is misleading and incorrect.

  3. Adding the exponents will create an equivalent expression.
    False. This statement does not apply here because there are no additional bases or terms to add exponents to; we only have \((r - 4)^3\).

  4. Multiplying the exponents will create an equivalent expression.
    False. Similar to the previous point, multiplying the exponents does not apply in this case. The expression has the same base (which is \(r - 4\)) and a single exponent of \(3\).

  5. The expression simplifies to \(\frac{1}{r^7}\).
    False. The expression \((r - 4)^3\) does not simplify to \(\frac{1}{r^7}\). It remains as \((r - 4)^3\).

In summary, the only statement that applies is:

  • There are three factors of \(r - 4\).