Final answer:
Using the rules of exponents, the expression (10^4)(5^2)^3/(10^3)(5^3) simplifies to 10^1 * 5^3, which is 1250. None of the provided answer choices match this answer, indicating a possible error in the question.
Step-by-step explanation:
The student asked about the value of the expression (10^4)(5^2)^3/(10^3)(5^3). To solve this, we can use the rules of exponents. First, we simplify the expression by using the power of a power rule, which means we multiply the exponents inside the parentheses. So, (5^2)^3 becomes 5^(2*3), or 5^6. Likewise, note that when powers of 10 are multiplied together, the powers are added, so (10^4) multiplied by any power of 10 just adds exponents. However, in this case, we are dealing with division, not multiplication.
Using the rule that says when we divide exponents with the same base, we subtract the exponents, the expression simplifies to 10^(4-3) * 5^(6-3) which equals 10^1 * 5^3. After simplification, this yields 10 * 125, or 1250. However, none of the answer choices match 1250, which suggests a possible typo or misunderstanding in the question as presented.