Question

Joe bought a rectangular farm. The length of his farm is $2^5\text{ft}$ and the width is $3^5\text{ft}$. What is the area of Joe's farm?

Answer 1

We know:
$\text{Area of a rectangle}=\text{Length}\times \text{Width}$

Given:
Length of the farm $=2^5\text{ft}$
Width of the farm $=3^5\text{ft}$
$\therefore$ Area of the farm $=(2^5\times 3^5){\text{ft}}^2$

To calculate $2^5\times 3^5,$ we need to follow the rule for the multiplication of exponents with the same exponent $\left(5\right)$ and different bases $(2,3)$.

Applying the exponent rule $a^n\times b^n=(a\times b{)}^n,$ we get:

Area of the farm
$=(2^5\times 3^5){\text{ft}}^2$
$=(2\times 3{)}^5=6^5{\text{ft}}^2$
$=(6\times 6\times 6\times 6\times 6){\text{ft}}^2$
$=7776{\text{ft}}^2$

Hence,
$\text{Area of the farm}=7776f{t}^2$