Let's go through the solution step by step.
### Step 1: Rewrite the Expression Using Properties of Exponents
Consider the initial expression:
[tex]\[
\left(11 j^{-3} k^{-2}\right) \left(j^3 k^4\right)
\][/tex]
We can use the properties of exponents to simplify the expression:
- [tex]\( j^{-3} \cdot j^3 \)[/tex]
- [tex]\( k^{-2} \cdot k^4 \)[/tex]
Using the property [tex]\( x^a \cdot x^b = x^{a+b} \)[/tex]:
1. [tex]\( j^{-3} \cdot j^3 = j^{-3+3} = j^0 = 1 \)[/tex]
2. [tex]\( k^{-2} \cdot k^4 = k^{-2+4} = k^2 \)[/tex]
Thus, the expression simplifies to:
[tex]\[
11 \cdot 1 \cdot k^2 = 11k^2
\][/tex]
### Step 2: Evaluate the Rewritten Expression
Now, we evaluate the simplified expression [tex]\( 11k^2 \)[/tex] using the given values [tex]\( j = -8 \)[/tex] and [tex]\( k = 7 \)[/tex]. Notice that [tex]\( j \)[/tex] is no longer in the expression due to the simplification.
So we substitute [tex]\( k = 7 \)[/tex] into the simplified expression:
[tex]\[
11k^2 = 11 \cdot (7^2) = 11 \cdot 49 = 539
\][/tex]
### Step 3: Complete the Statement
When [tex]\( j = -8 \)[/tex] and [tex]\( k = 7 \)[/tex], the original expression evaluates to:
[tex]\[
\boxed{539}
\][/tex]
