Answer :

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]