Question

simplify the expression \\(\frac{-5^8}{-5^4}\\). write your answer using only positive exponents. the solution is \\(\boxed{}\\).

Explanation:

Step1: Simplify the negative signs

The negative signs in the numerator and denominator cancel out. So we have $\frac{5^{8}}{5^{4}}$.

Step2: Use the quotient rule for exponents

The quotient rule states that $\frac{a^{m}}{a^{n}} = a^{m - n}$ (where $a
eq0$ and $m,n$ are real numbers). Here, $a = 5$, $m = 8$, and $n = 4$. So we calculate $8-4 = 4$. Thus, $5^{8 - 4}=5^{4}$.

Step3: Calculate $5^{4}$

$5^{4}=5\times5\times5\times5 = 625$.

Answer:

$5^{4}$ (or 625)