Final answer:
The expression 4x4x4x5x5 in index notation is written as 4^3 x 5^2, which represents 4 multiplied by itself three times and 5 multiplied by itself two times.
Step-by-step explanation:
The expression 4x4x4x5x5 can be represented in index notation by identifying the repeated multiplication of the same numbers. In this case, we have the number 4 being multiplied by itself three times, and the number 5 being multiplied by itself twice.
The index notation for the number 4 multiplied by itself three times is 4^3, and for the number 5 multiplied by itself two times, it is 5^2. Therefore, the given expression in index notation is 4^3 x 5^2.
This makes calculations much simpler and also saves space when writing lengthy numerical expressions.