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.

Explanation:

Step1: Recall the formula for the area of a rectangle

The area formula for a rectangle is \(A = \text{length}\times\text{width}\).

Step2: Substitute the given values into the formula

Given length \(l = 5^{3}\) and width \(w = 5^{2}\). Then \(A=5^{3}\times5^{2}\).

Step3: Use the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\)

Here \(a = 5\), \(m = 3\), \(n = 2\). So \(A=5^{3 + 2}\).

Answer:

\(5^{5}\)