Chapter 5.1, Problem 11OE

To determine

To find: Simplify the given expression.

Answer to Problem 11OE

  $\frac{{\left(x^2\right)}^3}{x^5}=x$

Explanation of Solution

Given information:

  $\frac{{\left(x^2\right)}^3}{x^5}$

Concept:

Using law of exponents

  $\frac{a^m}{a^n}=a^{m-n}$

  ${\left(a^m\right)}^n=a^{mn}$

Where $a$ be any value.

  $\frac{{\left(x^2\right)}^3}{x^5}$

  $\begin{array}{l}\Rightarrow \frac{{\left(x^2\right)}^3}{x^5}=\frac{x^{2\times 3}}{x^5}\\ \Rightarrow \frac{{\left(x^2\right)}^3}{x^5}=\frac{x^6}{x^5}\\ \Rightarrow \frac{{\left(x^2\right)}^3}{x^5}=x^{6-5}\\ \Rightarrow \frac{{\left(x^2\right)}^3}{x^5}=x\end{array}$

Therefore,

  $\frac{{\left(x^2\right)}^3}{x^5}=x$