Question
The rectanglar top of his table has an area of 3^7 square inches and a length of 3^4 inches. What is the width of the table top
Answers
GPT-4o mini
To find the width of the table top, we can use the formula for the area of a rectangle, which is given by:
\[
\text{Area} = \text{length} \times \text{width}
\]
We are given the area of the rectangle as \( 3^7 \) square inches and the length as \( 3^4 \) inches. We can let the width be \( w \).
Substituting the known values into the area formula, we have:
\[
3^7 = 3^4 \times w
\]
To solve for \( w \), we can divide both sides of the equation by \( 3^4 \):
\[
w = \frac{3^7}{3^4}
\]
Using the properties of exponents, specifically that \( \frac{a^m}{a^n} = a^{m-n} \), we can simplify the right side:
\[
w = 3^{7-4} = 3^3
\]
We can further calculate \( 3^3 \):
\[
3^3 = 27
\]
Therefore, the width of the table top is:
\[
\boxed{27} \text{ inches}
\]
\[
\text{Area} = \text{length} \times \text{width}
\]
We are given the area of the rectangle as \( 3^7 \) square inches and the length as \( 3^4 \) inches. We can let the width be \( w \).
Substituting the known values into the area formula, we have:
\[
3^7 = 3^4 \times w
\]
To solve for \( w \), we can divide both sides of the equation by \( 3^4 \):
\[
w = \frac{3^7}{3^4}
\]
Using the properties of exponents, specifically that \( \frac{a^m}{a^n} = a^{m-n} \), we can simplify the right side:
\[
w = 3^{7-4} = 3^3
\]
We can further calculate \( 3^3 \):
\[
3^3 = 27
\]
Therefore, the width of the table top is:
\[
\boxed{27} \text{ inches}
\]