Sure, let's simplify the given expression step-by-step:
The given expression is:
[tex]\[
(18 u^8 v^{-3})(4 u^{-2} v^5)
\][/tex]
### Step 1: Combine the Coefficients
First, we multiply the coefficients (the numeric values) from each part of the expression:
[tex]\[
18 \cdot 4 = 72
\][/tex]
### Step 2: Combine the Powers of [tex]\(u\)[/tex]
Next, we handle the variable [tex]\(u\)[/tex]. We use the property of exponents which states that [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex]:
[tex]\[
u^8 \cdot u^{-2} = u^{8 + (-2)} = u^6
\][/tex]
### Step 3: Combine the Powers of [tex]\(v\)[/tex]
Similarly, we handle the variable [tex]\(v\)[/tex]. Using the same property of exponents:
[tex]\[
v^{-3} \cdot v^5 = v^{-3 + 5} = v^2
\][/tex]
### Step 4: Write the Final Expression
Combining all these results, we get the simplified form of the original expression:
[tex]\[
72 u^6 v^2
\][/tex]
So, the given expression [tex]\((18 u^8 v^{-3})(4 u^{-2} v^5)\)[/tex] simplifies to:
[tex]\[
72 u^6 v^2
\][/tex]
