Sure, let's simplify the given expression step-by-step: [tex]\(-4 x^8 / 2 x^2\)[/tex].
### Step 1: Simplify the Coefficients
The coefficients in the expression are -4 and 2. We need to divide these two coefficients:
[tex]\[
\frac{-4}{2} = -2
\][/tex]
### Step 2: Simplify the Exponents
Next, we need to simplify the exponents of [tex]\(x\)[/tex]. The expression has [tex]\(x^8\)[/tex] in the numerator and [tex]\(x^2\)[/tex] in the denominator. Using the laws of exponents, specifically the quotient of powers property, which states:
[tex]\[
\frac{x^m}{x^n} = x^{m-n}
\][/tex]
we get:
[tex]\[
\frac{x^8}{x^2} = x^{8-2} = x^6
\][/tex]
### Step 3: Combine the Simplified Parts
We now combine the simplified coefficient and the simplified variable expression:
[tex]\[
-2 \cdot x^6 = -2x^6
\][/tex]
Thus, the simplified expression is:
[tex]\[
-2x^6
\][/tex]
This is the final simplified form of [tex]\(-4 x^8 / 2 x^2\)[/tex].
