Chapter 12, Problem 2CLR

To determine

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

Answer to Problem 2CLR

The value of the expression ${(b÷d+e)}^a$ is $-\frac{2}{13}$ .

Explanation of Solution

Given information:

The expression is ${(b÷d+e)}^a$ 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 plugged in the expression.

The expression within the parentheses should be simplified first.

When parentheses is not present order of simplification must be division first then subtraction.

Calculation:

Consider the expression ${(b÷d+e)}^a$ 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 ${(b÷d+e)}^a$ replace as:

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

Again recall that the expression within the parentheses should be simplified first,

Therefore, $1÷3-\frac{5}{2}$ must be simplified first.

But we know that when parentheses is not present order of simplification must be division first then subtraction.

Follow the rule,

  $\begin{array}{c}1÷3-\frac{5}{2}=\frac{1}{3}-\frac{5}{2}\\ =\frac{2-15}{6}\\ =-\frac{13}{6}\end{array}$

Further simplify,

  $\begin{array}{c}{\left(-\frac{13}{2}\right)}^{-1}=\frac{1}{{\left(-\frac{13}{2}\right)}^1}\\ =-\frac{2}{13}\end{array}$

Thus, the value of the expression ${(b÷d+e)}^a$ is $-\frac{2}{13}$ .