Simplify the Power Expression: 5^7 ÷ 5^10

To solve the expression $\frac{5^7}{5^{10}}$, we need to apply the Power of a Quotient Rule for Exponents. This rule states that when dividing like bases, you subtract the exponents:

$\frac{a^m}{a^n} = a^{m-n}$.

In this particular case, the base is 5, and the exponents are 7 and 10. Using the rule, we subtract the exponent in the denominator from the exponent in the numerator:

• Numerator exponent = 7
• Denominator exponent = 10

Therefore, we get:

$5^{7-10}$.

In conclusion, the simplified form of the given expression is:
$5^{-3}$.

The solution to the question is: $5^{7-10}$.