Chapter 12, Problem 53CUR

To determine

To find: The product of $r^{-8}\cdot r^6$ and the express the result in positive exponents.

Answer to Problem 53CUR

The value of the expression is ${\left(r^{-1}\right)}^2$ or $\frac{1}{r^2}$

Explanation of Solution

Given information : The expression is $r^{-8}\cdot r^6$

Formula used : $a^m\cdot a^n=a^{m+n}$

Calculation :

  $r^{-8}\cdot r^6=r^{\left(-8+6\right)}=r^{-2}={\left(r^{-1}\right)}^2=\frac{1}{r^2}$

Thus, the value of the expression is ${\left(r^{-1}\right)}^2$ or $\frac{1}{r^2}$