Chapter 4.3, Problem 29IP

To determine

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

Answer to Problem 29IP

The product is , ${\text{m}}^{-5}.\left(-{\text{4m}}^6\right)=-4\text{m }$

Explanation of Solution

Given information: The expression is, ${\text{m}}^{-5}.\left(-{\text{4m}}^6\right)$

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,

  $\begin{array}{l}{\text{m}}^{-5}.\left(-{\text{4m}}^6\right)=-4.{\text{m}}^{-5}.{\text{m}}^6\\ =-4{\text{m}}^{-5+6}\left(\text{Product of the powers property; the common base is m }\right)\\ =-4\text{m }\left(\text{Add the exponents}\right).\end{array}$

Hence,the product is ${\text{m}}^{-5}.\left(-{\text{4m}}^6\right)=-4\text{m }$