Simplify the following expression, writing the answer using index notation: 12×12212×12 2

To simplify the expression $12 \times 12^{2} \times 12^{2}$ using index notation, we can follow these steps:

1. Break Down the Problem

We have the expression: $12 \times 12^{2} \times 12^{2}$ This can be understood as multiplying together different powers of the same base $12$.

2. Relevant Concepts

In index notation, when multiplying powers with the same base, we add the exponents: $a^{m} \times a^{n} = a^{m+n}$

3. Analysis and Detail

Let's rewrite the expression in index notation:

1. The first term $12$ can be written as $12^{1}$.
2. The expression now becomes: $12^{1} \times 12^{2} \times 12^{2}$
3. Now we can add the exponents: $1 + 2 + 2 = 5$
4. Thus, we can express this as: $12^{5}$

4. Verify and Summarize

We have confirmed that the powers have been correctly calculated and combined. The simplified expression in index notation is:

Final Answer

$12^{5}$