Question

1. what is the width of the rectangle written as an exponential expression? 2^(-1) m area = 2^(-4) m^2 ? m

Explanation:

Step1: Recall area formula

The area formula for a rectangle is $A = l\times w$, where $A$ is area, $l$ is length and $w$ is width. We know $A = 2^{-4}$ and $l=2^{-1}$, and we need to find $w$. So $w=\frac{A}{l}$.

Step2: Substitute values and use exponent rule

Substitute the values of $A$ and $l$ into the width - formula: $w=\frac{2^{-4}}{2^{-1}}$. According to the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, here $a = 2$, $m=-4$ and $n = - 1$. Then $w=2^{-4-(-1)}$.

Step3: Simplify the exponent

Simplify the exponent: $-4-(-1)=-4 + 1=-3$. So $w = 2^{-3}$ m.

Answer:

$2^{-3}$ m