Chapter 4.3, Problem 7GP

To determine

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

Answer to Problem 7GP

The product is , ${\text{m}}^8.{\text{m}}^{-10}=\frac{1}{{\text{m}}^2}$

Explanation of Solution

Given information: The expression is, ${\text{m}}^8.{\text{m}}^{-10}$

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,

  $\begin{array}{l}{\text{m}}^8.{\text{m}}^{-10}=m^{8+\left(-10\right)}\left(\text{Product of the powers property; the common base is m }\right).\\ ={\text{m}}^{-2}\left(\text{Add the exponents}\right).\\ =\frac{1}{{\text{m}}^2}\end{array}$

Hence,the product is ${\text{m}}^8.{\text{m}}^{-10}=\frac{1}{{\text{m}}^2}$