Question

a rectangle has a length of 5^3 units and a width of 5^2 units. what is the area of the rectangle? write your answer as a power of 5. (type your answer using exponential notation.) click on the icon to view area formulas for several shapes.

Explanation:

Step1: Recall area formula

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l = 5^{3}$ and $w=5^{2}$.

Step2: Use exponent - multiplication rule

When multiplying two numbers with the same base $a^{m}\times a^{n}=a^{m + n}$. So, $A=5^{3}\times5^{2}=5^{3 + 2}$.

Step3: Calculate the exponent sum

$3+2 = 5$, so $A = 5^{5}$.

Answer:

$5^{5}$