Question

Evaluate the expression ${\left(3-4^2\right)}^2+8$.

Short answer

The value of the expression of ${\left(3-4^2\right)}^2+8$is 177.

Step-by-step solution

Step 1. Apply the BODMAS rule.

According to the BODMAS rule of simplification, at first, the bracket operation must be completed followed division, by multiplication, addition, and finally subtraction.

Step 2. Example of applying BODMAS rule.

The expression$2+[10-{(3+1)}^2]-10$ can be written as

$\begin{array}{l}2+[10-{(3+1)}^2]-10=2+[10-4^2]-10\\ =2+[10-16]-10\\ =2-6-10\\ =2-16\\ =-14\end{array}$

Step 3. Description of step.

The given expression is${\left(3-4^2\right)}^2+8$

First, solving the addition and power inside the bracket

$\begin{array}{l}{\left(3-4\times 4\right)}^2+8\\ {\left(3-16\right)}^2+8\\ {\left(-13\right)}^2+8\\ \text{Solvingthepower}\\ \left(-13\right)\times \left(-13\right)+8\\ 169+8\\ 177\end{array}$