Chapter 4.3, Problem 8GP

To determine

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

Answer to Problem 8GP

The product is , ${\text{y}}^{-4}.{\text{y}}^{12}={\text{y}}^8$

Explanation of Solution

Given information: The expression is, ${\text{y}}^{-4}.{\text{y}}^{12}$

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,

  $\begin{array}{l}{\text{y}}^{-4}.{\text{y}}^{12}={\text{y}}^{-4+12}\left(\text{Product of the powers property; the common base is y }\right).\\ ={\text{y}}^8\left(\text{Add the exponents}\right).\end{array}$

Hence,the product is ${\text{y}}^{-4}.{\text{y}}^{12}={\text{y}}^8$