Chapter 4.4, Problem 12OE

a.

To determine

To Simplify: The given expression.

Answer to Problem 12OE

Simplest form is $x^{10}$

Explanation of Solution

Given information: ${[{(-x)}^5]}^2$

Formula used: Product of power rule of exponent ${(ab)}^m=a^m{b}^m$ and power rule of exponent ${(a^m)}^n=a^{mn}$

Calculation:

Using power rule,

  ${[{(-x)}^5]}^2=[{(-x)}^{5*2}]$

Simplify the exponents,

  $[{(-x)}^{10}]$

Using product of power rule of exponents

  ${(-1)}^{10}{x}^{10}$

Simplify it further,

  $\begin{array}{l}1*x^{10}\\ x^{10}\end{array}$

b.

To determine

To Simplify: The given expression.

Answer to Problem 12OE

Simplest form is $x^{10}$

Explanation of Solution

Given information: ${[{(-x)}^2]}^5$

Rule used: Product of power rule of exponent ${(ab)}^m=a^m{b}^m$ and power rule of exponent ${(a^m)}^n=a^{mn}$

Calculation:

Using power rule,

  ${[{(-x)}^2]}^5=[{(-x)}^{2*5}]$

Simplify the exponents,

  $[{(-x)}^{10}]$

Using product of power rule of exponents

  ${(-1)}^{10}{x}^{10}$

Simplify it further,

  $\begin{array}{l}1*x^{10}\\ x^{10}\end{array}$