Chapter 9.6, Problem 31PPS

(a)

To determine

The simplified expression for the given terms

Answer to Problem 31PPS

  $\begin{array}{l}4x^4\\ 16x^8\end{array}$

Explanation of Solution

Given:

The given terms are

  ${\left(2x^2\right)}^2\text{and }{\left[{\left(2x^2\right)}^2\right]}^2$

Calculation:

The terms can be simplified as

  $\begin{array}{l}={\left(2x^2\right)}^2\\ ={\left(2\right)}^2{\left(x^2\right)}^2\\ =4x^4\\ \text{and }\\ \text{=}{\left[{\left(2x^2\right)}^2\right]}^2\\ \text{=}{\left(2x^2\right)}^4\\ \text{=}{\left(2\right)}^4{\left(x^2\right)}^4\\ \text{=}16x^8\end{array}$

(b)

To determine

The graph of the given terms

Answer to Problem 31PPS

  

  

Explanation of Solution

Given:

The given terms are

  ${\left(2x^2\right)}^2\text{and }{\left[{\left(2x^2\right)}^2\right]}^2$

Calculation:

The terms can be simplified as

  $\begin{array}{l}={\left(2x^2\right)}^2\\ ={\left(2\right)}^2{\left(x^2\right)}^2\\ =4x^4\end{array}$

The graph will be

  

  $\begin{array}{l}\text{and }\\ \text{=}{\left[{\left(2x^2\right)}^2\right]}^2\\ \text{=}{\left(2x^2\right)}^4\\ \text{=}{\left(2\right)}^4{\left(x^2\right)}^4\\ \text{=}16x^8\end{array}$

The graph will be

  

(c)

To determine

Similarities and difference in the graphs

Explanation of Solution

Given:

The given terms are

  ${\left(2x^2\right)}^2\text{and }{\left[{\left(2x^2\right)}^2\right]}^2$

Calculation:

The graph are

  

  

Similarities:

• Both the graphs are non linear
• Both the graphs meet the x axis at origin and does not exist below the origin
• Both the graphs are upper parabola

Differences:

• The slopes of both the graph is different
• One graph is for degree 4 and other is for degree 8