Final answer:
To solve the mathematical problem completely, we rewrite 2 x 2 x 3 x 3 x 3 x 5 as 2^2 x 3^3 x 5 by identifying the base numbers and their corresponding exponents, which indicate the number of times each base number is used as a factor in the product.
Step-by-step explanation:
When faced with the task to rewrite the number strings using exponents like the number string 2 x 2 x 3 x 3 x 3 x 5, the goal is to simplify the expression by identifying the base numbers and how many times each base number is multiplied by itself. This is the concept of exponentiation where a number, known as the base, is multiplied by itself a certain number of times indicated by the exponent.
Here's how to solve the mathematical problem completely:
The number 2 appears twice, so we express it as 22.
The number 3 appears three times, so we express it as 33.
The number 5 appears once, and any number to the first power is just itself, so we keep it as 5.
Combining these, we get 22 x 33 x 5.
Understanding how to work with exponents is essential in mathematics, especially in algebra and higher-level math courses. By rewriting expressions with exponents, we can make them more concise and ready for further mathematical operations such as multiplication or division of exponentials, where we apply rules like multiplying the digit terms and adding the exponents for the same base, as seen in examples provided.