To find the width of the rectangle, we can use the formula for the area of a rectangle, which is given by:
\[ \text{Area} = \text{Length} \times \text{Width} \]
We know the area and the length, so we can rearrange the formula to find the width:
\[ \text{Width} = \frac{\text{Area}}{\text{Length}} \]
Given that the area of the rectangle is \( 15w^6w^9 \) and the length is \( 8wb^5 \), we first need to simplify the area term.
The area \( 15w^6w^9 \) can be combined by adding the exponents of \( w \):
\[ 15w^{6+9} = 15w^{15} \]
Now we can substitute the area and length into the equation for width:
\[ \text{Width} = \frac{15w^{15}}{8wb^5} \]
We can simplify this expression by dividing both the coefficients and the powers of \( w \):
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Divide the coefficients: \[ \frac{15}{8} \]
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For the \( w \) terms, we have \( w^{15} \) divided by \( w \): \[ w^{15-1} = w^{14} \]
Therefore, the width can be simplified to:
\[ \text{Width} = \frac{15}{8} w^{14} b^{-5} \]
This can also be written as:
\[ \text{Width} = \frac{15}{8} \cdot \frac{w^{14}}{b^5} \]
Thus, the width of the rectangle is:
\[ \frac{15}{8} \cdot \frac{w^{14}}{b^5} \]