Question

simplify.
rewrite the expression in the form $5^n$.
\\(\dfrac{5^{-5}}{5^8} = \\) \boxed{\dfrac{-x}{+x}}

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base \( \frac{a^m}{a^n}=a^{m - n} \), here \( a = 5 \), \( m=- 5 \), \( n = 8 \).

Step2: Apply the rule

\( \frac{5^{-5}}{5^{8}}=5^{-5-8} \)
Calculate \( - 5-8=-13 \), so the expression becomes \( 5^{-13} \).

Answer:

\( 5^{-13} \)