Question

#10 i simplify the expression \\(\frac{-5^{8}}{-5^{4}}\\). write your answer using only positive exponents.

Explanation:

Step1: Use exponent rule $\frac{a^m}{a^n}=a^{m - n}$

We have the expression $\frac{-5^{8}}{-5^{4}}$. The negative signs in the numerator and denominator will cancel out (since $\frac{-a}{-b}=\frac{a}{b}$ for non - zero $a$ and $b$), so we can focus on simplifying $\frac{5^{8}}{5^{4}}$.
Using the rule $\frac{a^m}{a^n}=a^{m - n}$ where $a = 5$, $m=8$ and $n = 4$, we get $5^{8-4}$.

Step2: Calculate the exponent

Calculate $8 - 4=4$. So the expression simplifies to $5^{4}$.
We can also calculate $5^{4}=5\times5\times5\times5 = 625$.

Answer:

$5^{4}$ (or $625$)