Chapter 6.1, Problem 36E

To determine

To correct:The error in the expression

  $\begin{array}{l}\frac{x^5\cdot x^3}{x^4}=\frac{x^8}{x^4}\\ =x^{\raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\\ =x^2\end{array}$

Answer to Problem 36E

The correct expression is $\frac{x^5\cdot x^3}{x^4}=x^4$

Explanation of Solution

Given information:The incorrect expression

  $\begin{array}{l}\frac{x^5\cdot x^3}{x^4}=\frac{x^8}{x^4}\\ =x^{\raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\\ =x^2\end{array}$

Calculation:The product rule of exponents is given as,

  $a^y\cdot a^z=a^{y+z}$ , for any arbitrary a, yand z

The division rule of exponents is given as,

  $\frac{a^y}{a^z}=a^{y-z}$ , for any arbitrary a, yand z

The error in the given expression is in the step where it is written as $\frac{x^8}{x^4}=x^{\raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}=x^2$ instead of $\frac{x^8}{x^4}=x^{8-4}=x^4$.

Thus, the correct solution will be,