Final answer:
The repeated multiplication 2x2x2x2x5x5x5 can be expressed in exponential form as 2^4 x 5^3, where 2^4 represents 2 multiplied by itself four times and 5^3 represents 5 multiplied by itself three times.
Step-by-step explanation:
The student's question asks to write repeated multiplication in exponential form. The expression given is 2x2x2x2x5x5x5. Each base number (2 and 5) is multiplied by itself a certain number of times, which makes it possible to write them as exponents. The base number 2 appears four times and the base number 5 appears three times.
To write this expression in exponential form, we combine the like terms and use exponents to represent the repeated multiplication. Thus, the expression 2x2x2x2x5x5x5 is written in exponential form as 2^4 x 5^3. Here, 2^4 signifies that 2 is multiplied by itself four times, and 5^3 signifies that 5 is multiplied by itself three times. This conversion simplifies the expression without altering its value, and does so without requiring any simplification or computation of the actual product.