Question

The area of a rectangle is 15w^6w^9 if the length of the rectangle is 8wb^5, what is the width

Answer 1

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 \( w \):

1. Divide the coefficients:
\[
\frac{15}{8}
\]

2. 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:

\[
\frac{15}{8} \cdot \frac{w^{14}}{b^5}
\]