Chapter 7.9, Problem 3MRE

To determine

To calculate: The simplified form of the expression ${\left(\frac{-3p}{q}\right)}^2$ and state restrictions on variable.

Answer to Problem 3MRE

The simplified value of the expression ${\left(\frac{-3p}{q}\right)}^2$ is $\frac{9p^2}{q^2}$ and restriction is $q\ne 0$ .

Explanation of Solution

Given information:

The expression ${\left(\frac{-3p}{q}\right)}^2$ .

Formula used:

The simplest form of an algebraic fraction is when numerator and denominator have no common factor other than 1 and $-1$ .

Calculation:

Consider the expression ${\left(\frac{-3p}{q}\right)}^2$ .

Recall that the simplest form of an algebraic fraction is when numerator and denominator have no common factor other than 1 and $-1$ .

Apply it,

  $\begin{array}{c}{\left(\frac{-3p}{q}\right)}^2=\frac{{\left(-3\right)}^2{\left(p\right)}^2}{{\left(q\right)}^2}\\ =\frac{9p^2}{q^2}\end{array}$

To restrict the variable, exclude the value that makes the denominator zero.

The denominator will be zero when $\begin{array}{c}{q}^2=0\\ q=0\end{array}$ .

For denominator not to be zero, $q\ne 0$ .

Thus, the simplified value of the expression ${\left(\frac{-3p}{q}\right)}^2$ is $\frac{9p^2}{q^2}$ and restriction is $q\ne 0$ .