Chapter 4.3, Problem 21IP

To determine

To find the product and express the result using positive exponents.

Answer to Problem 21IP

The product is , ${\text{a}}^7.{\text{a}}^2{\text{ = a}}^9$

Explanation of Solution

Given information: The expression is, ${\text{a}}^7.{\text{a}}^2$

Concept used: The products of powers property is defined by,

Multiply powers with the same base by adding their exponents.

  $a^m.a^n=a^{m+n}$

Calculation : The product of the numbers is obtained as,

  $\begin{array}{l}{\text{a}}^7.{\text{a}}^2={\text{a}}^{7+2}\left(\text{Product of the powers property; the common base is a }\right).\\ {\text{ = a}}^9\left(\text{Add the exponents}\right).\end{array}$

Hence,the product is ${\text{a}}^7.{\text{a}}^2{\text{ = a}}^9$