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Question 7 of 10

Which of the following would you do if you were to 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?

Check all that apply.

A. You would write [tex]12^3[/tex].

B. You would use 12 as the base and 3 as the exponent.

C. You would write [tex]3^{12}[/tex].

D. You would use 3 as the base and 12 as the exponent.

Sagot :

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.