To write the expression [tex]\(3 \times 3 \times 3 \times 3 \times 3 \times 3\)[/tex] using exponents, we need to follow these steps:
1. Identify the base and the exponent:
- The "base" is the number being multiplied, which is 3.
- The "exponent" is the number of times the base is multiplied by itself. Here, the exponent is 6, because there are six 3's being multiplied together.
2. Express the repeated multiplication using the base and exponent:
- The repeated multiplication [tex]\(3 \times 3 \times 3 \times 3 \times 3 \times 3\)[/tex] can be written as [tex]\(3^6\)[/tex].
Now, let's compare this exponential form [tex]\(3^6\)[/tex] with the given choices:
- A. [tex]\(3^6\)[/tex]
- B. [tex]\(6^3\)[/tex]
- C. [tex]\(12^3\)[/tex]
- D. [tex]\(9^4\)[/tex]
The correct choice that matches [tex]\(3^6\)[/tex] is:
A. [tex]\(3^6\)[/tex]
Therefore, the expression [tex]\(3 \times 3 \times 3 \times 3 \times 3 \times 3\)[/tex] written using exponents is [tex]\(3^6\)[/tex], which corresponds to option A.
