Question

karim builds a wooden table.

the rectangular 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?

9 inches
27 inches
2,187 inches
59,049 inches

Explanation:

Set up the area formula for a rectangle

$$ \text{Area} = \text{length} \times \text{width} $$

$$ 3^7 = 3^4 \times w $$

Solve for the width using the quotient of powers rule

$$ w = \frac{3^7}{3^4} = 3^{7-4} = 3^3 $$

Evaluate the exponential expression

$$ w = 3 \times 3 \times 3 = 27 $$

Answer:

• (A) 9 inches
• (B) 27 inches (Correct answer)
• (C) 2,187 inches
• (D) 59,049 inches