Final answer:
Options A and B correctly represent 10^5, which is 100,000. Option A is 10 multiplied by itself five times, and option B is the numerical value. When multiplying powers of 10, the exponents are added together.
Step-by-step explanation:
The question 'Which of the following correctly represents 10^5?' pertains to understanding powers of 10 and exponential notation—an essential concept in middle school mathematics. Option A, which is '10 * 10 * 10 * 10 * 10', and option B, which is '100,000', both correctly represent 10^5.
To further explain, the expression 10^5 means the number 10 is multiplied by itself a total of five times. Indeed, 10 * 10 * 10 * 10 * 10 is 100,000. On the other hand, option C, '10 * 5', is simply 50, and option D, '10,000', is 10^4. Additionally,
when calculating products involving powers of 10, remember that the exponents are added when the bases are the same, for instance, 10^2 * 10^3 equals 10^5. Furthermore, applying this rule helps simplify calculations without using a calculator. For example, multiplying 4.506 * 10^4 by 1.003 * 10^2 equals 4.506 * 1.003 * 10^(4+2), which is approximately 4.516518 * 10^6 in proper scientific notation.