Question

a circle has a radius of 5^4 units. what is the area of the circle? write your answer using a power of 5. (type your answer using exponential notation. type an exact answer in terms of π.)

Explanation:

Step1: Recall area formula for circle

The formula for the area of a circle is $A = \pi r^{2}$, where $r$ is the radius of the circle.

Step2: Substitute given radius

Given $r = 5^{4}$, then $A=\pi\times(5^{4})^{2}$.

Step3: Simplify the exponent

Using the power - of - a - power rule $(a^{m})^{n}=a^{mn}$, so $(5^{4})^{2}=5^{4\times2}=5^{8}$. Then $A = \pi\times5^{8}$.

Answer:

$\pi\times5^{8}$