To solve the given question and write the expression [tex]\(3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3\)[/tex] using an exponent, follow these steps:
1. Identify the repetition of the base number: Observe that the number 3 is repeatedly multiplied by itself.
2. Count the number of times the base appears: Determine how many times the number 3 appears in the multiplication expression. Here, it appears 12 times.
3. Form the exponential expression:
- The base (number being multiplied) is 3.
- The exponent (number of times the base is multiplied by itself) is 12.
Putting this information together, you would write the expression as [tex]\(3^{12}\)[/tex].
Thus:
- Statement (A) suggests writing [tex]\(12^3\)[/tex], which is incorrect.
- Statement (B) suggests using 12 as the base and 3 as the exponent, which is incorrect.
- Statement (C) suggests writing [tex]\(3^{12}\)[/tex], which is correct.
- Statement (D) suggests using 3 as the base and 12 as the exponent, which is correct.
Therefore, the correct choices are C and D.
