Certainly! Let's simplify the given expression step-by-step and express it in index form.
Given expression:
[tex]\[ 4 \times 4 \times 4 \times 4 \times 4 \times 4 \][/tex]
1. First, observe that the number 4 is being multiplied by itself multiple times.
2. To express repeated multiplication of the same number in index form, we use exponents.
In this case:
- The base number is 4.
- The number of times 4 is multiplied by itself is 6.
Using this information, we can write the expression in index form as:
[tex]\[ 4^6 \][/tex]
Now, let's calculate the value of [tex]\( 4^6 \)[/tex]:
[tex]\[ 4^6 = 4096 \][/tex]
Therefore, the simplified expression in index form is:
[tex]\[ 4^6 = 4096 \][/tex]
So, the final answer is:
[tex]\[ 4^6 = 4096 \][/tex]
