Question

The area of a rectangle is 16w^6w^9 if the length of the rectangle is 8wb^5, what is the width?
Give me the coefficient followed by the exponent of w and then b

Answer 1

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**