Final answer:
The expression 5^3/5^7 simplifies to 5^-4 by subtracting the exponents because they share the same base, according to the rules for division of powers.
Step-by-step explanation:
Simplifying Powers with the Same Base
When simplifying the expression 53/57, we apply the rule for division of powers with the same base. According to this rule, we subtract the exponent of the denominator from the exponent of the numerator. Thus, the simplification process would look like this:
Start with the original expression: 5^3/5^7.
Subtract the exponents, since they have the same base of 5:
3 - 7
= -4.
Write the result in index form: 5^-4.
Therefore, the simplified form of the expression 5^3/5^7 in index form is 1/5^4.