To find the width of the rectangle, we can use the formula for the area of a rectangle:
\[ \text{Area} = \text{length} \times \text{width} \]
We are given:
- Area = \(16w^6w^9\)
- Length = \(8wb^5\)
We can find the width by rearranging the area formula:
\[ \text{width} = \frac{\text{Area}}{\text{length}} \]
Substituting the values:
\[ \text{width} = \frac{16w^6w^9}{8wb^5} \]
First, let's simplify the expression for the width. We can combine the powers of \(w\) in the numerator:
\[ w^6 \cdot w^9 = w^{6+9} = w^{15} \]
So now the area can be rewritten as:
\[ \text{Area} = 16w^{15} \]
Now substituting this back into the formula:
\[ \text{width} = \frac{16w^{15}}{8wb^5} \]
Now, we can simplify:
\[ \text{width} = \frac{16}{8} \cdot \frac{w^{15}}{w} \cdot \frac{1}{b^5} = 2 \cdot w^{15-1} \cdot b^{-5} = 2w^{14}b^{-5} \]
Thus, the width of the rectangle is:
\[ \text{width} = 2w^{14}b^{-5} \]
Now, we can identify the coefficient and the exponents:
- Coefficient: \(2\)
- Exponent of \(w\): \(14\)
- Exponent of \(b\): \(-5\)
So, the final answer is:
2, 14, -5