Simplify the Exponential Expression: 5³÷5⁸

We need to simplify the expression $\frac{5^3}{5^8}$ using the rules of exponents. Specifically, we will use the power of a quotient rule for exponents which states that when you divide like bases you subtract the exponents:

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

Here, the base is 5, the exponent in the numerator is 3, and the exponent in the denominator is 8.

• Apply the rule: $5^{3-8}$
• Subtract the exponents: $5^{-5}$.

Therefore, the simplified expression is $5^{-5}$.

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