To simplify the expression \(-25x^8 / 5x\) using the properties of exponents, we can follow these steps:
Step 1: Simplify the coefficients
First, simplify the numerical coefficients:
\[ -25 / 5 = -5 \]
Step 2: Apply the properties of exponents
Next, we apply the property of exponents that states:
\[ \frac{a^m}{a^n} = a^{m-n} \]
In our expression, we have \(x^8\) in the numerator and \(x\) (which is the same as \(x^1\)) in the denominator. We can simplify this as follows:
\[ \frac{x^8}{x^1} = x^{8-1} = x^7 \]
Step 3: Combine the simplified parts
Now we can combine the simplified coefficient and the simplified exponent:
\[ -25x^8 / 5x = -5x^7 \]
Final Expression
Thus, the simplified expression is:
\[ \boxed{-5x^7} \]