Chapter 12, Problem 5CLR

To determine

To Evaluate: The simplified value of the expression ${(de+ab)}^c$ where $a=-1$ , $b=1$ , $c=0$ , $d=3$ and $e=-\frac{5}{2}$ .

Answer to Problem 5CLR

The value of the expression ${(de+ab)}^c$ is $1$ .

Explanation of Solution

Given information:

The expression is ${(de+ab)}^c$ and the values of variables are $a=-1$ , $b=1$ , $c=0$ , $d=3$ and $e=-\frac{5}{2}$ .

Formula used:

An algebraic expression may be replaced by numerical expression when the value of variable

Plug into the expression.

Any real number to the power zero is one. That is,

  $x^0=1$

Where $x$ is any real number.

Calculation:

Consider the expression ${(de+ab)}^c$ and values of variable $a=-1$ , $b=1$ , $c=0$ , $d=1$ and $e=-\frac{5}{2}$ .

Recall that an algebraic expression may be replaced by numerical expression when the value of variable plugged in the expression.

Use it, the expression ${(de+ab)}^c$ replace as:

  ${\left(3\times \left(-\frac{5}{2}\right)+\left(-1\right)\times 1\right)}^0$

Again recall that any real number to the power zero is one. That is,

  $x^0=1$

Where $x$ is any real number.

Therefore,

  ${\left(3\times \left(-\frac{5}{2}\right)+\left(-1\right)\times 1\right)}^0=1$

Thus, the value of the expression ${(de+ab)}^c$ is $0$ .