Question

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

• A. $6^5$
• B. $6$
• C. ${1.5}^5$
• D. None of the above

Answer 1

The correct option is A $6^5$

We know:
Area of rectangle $=$ Length$\times$ Breadth

Given,
Length of farm $=2^5\text{ft}$
Breadth of farm $=3^5\text{ft}$
$\therefore$ Area of Joe's 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 same exponent $\left(5\right)$ and different bases $(2,3)$.

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

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

Therefore, option (a.) is the correct one.