Use Multiplication Properties of Exponents · Exercise 78

Email Kate emails a flyer to ten of her friends and tells them to forward it to ten of their friends, who forward it to ten of their friends, and so on. The number of people who receive the email on the second round is $10^2$, on the third round is $10^3$, as shown in the table below. How many people will receive the email on the sixth round? Simplify the expression to show the number of people who receive the email.

$$\begin{array}{cc}\text{Round}& \text{Number of people}\\ \text{1}& \text{10}\\ \text{2}& 10^2\\ \text{3}& 10^3\\ \text{…}& \text{…}\\ \text{6}& \text{?}\end{array}$$

This problem refers to a figure in its source book that isn't reproduced here.

OpenStax, Elementary Algebra 2e · §6.2 Use Multiplication Properties of Exponents · Exercise 78