Question

expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression -25x^8/5x

Answer 1

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:

\[
\boxed{-5x^7}
\]