Question

1. model with math what is the width of the rectangle written as an exponential expression? image: rectangle with area = 10⁴ m², side 10³ m, width? m

Explanation:

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \). We need to find the width \( w \), so we can rearrange the formula to \( w=\frac{A}{\text{length}} \).

Step2: Substitute given values

We know the area \( A = 10^{4}\, \text{m}^2 \) and the length \( l = 10^{3}\, \text{m} \). Substituting these into the formula for width, we get \( w=\frac{10^{4}}{10^{3}} \).

Step3: Apply exponent rule for division

When dividing exponents with the same base, we use the rule \( \frac{a^{m}}{a^{n}}=a^{m - n} \). Here, \( a = 10 \), \( m = 4 \), and \( n = 3 \). So \( \frac{10^{4}}{10^{3}}=10^{4 - 3}=10^{1} \).

Answer:

The width of the rectangle is \( 10^{1}\, \text{m} \) (or \( 10\, \text{m} \)).