Chapter 8.1, Problem 87CCR

To determine

The value of the expression $\frac{{\left(1-3\right)}^2}{{\left(4-2\right)}^2}$

Answer to Problem 87CCR

The value of the expression is $1$

Explanation of Solution

Given:

  $\frac{{\left(1-3\right)}^2}{{\left(4-2\right)}^2}$

Concept Used:

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation: In order to find the value of expression $\frac{{\left(1-3\right)}^2}{{\left(4-2\right)}^2}$ as below:

  $\begin{array}{c}{2}^2=2\ast 2=4\\ \text{So the experssion will become}\\ \frac{{\left(1-3\right)}^2}{{\left(4-2\right)}^2}\\ =\frac{{\left(-2\right)}^2}{{\left(2\right)}^2}\\ =1\end{array}$

Thus, the value of the expression is $1$