Question

simplify.
rewrite the expression in the form $5^{n}$.
$\frac{5^{-5}}{5^{8}} = \boxed{}$

Explanation:

Step1: Apply exponent division rule

When dividing exponents with the same base, subtract the denominator exponent from the numerator exponent: $\frac{a^m}{a^n}=a^{m-n}$
$\frac{5^{-5}}{5^8}=5^{-5-8}$

Step2: Calculate the exponent value

Compute the subtraction in the exponent:
$5^{-5-8}=5^{-13}$

Answer:

$5^{-13}$