Question

Find the value of each expression

8. $\left[6-{\left(12-8\right)}^2\right]÷5$

Short answer

Value of $\left[6-{\left(12-8\right)}^2\right]÷5$ is $-2$

Step-by-step solution

- Order for simplification 

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

- Simplify expression inside grouping symbol

To evaluate the value of the given expression, first simplify the expression inside the parenthesis and then expand the exponent. Then simplify further the expression in side bracket as shown below

$\begin{array}{c}\left[6-{\left(12-8\right)}^2\right]÷5=\left[6-{\left(4\right)}^2\right]÷5\\ =\left[6-16\right]÷5\\ =\left[-10\right]÷5\end{array}$

- Divide -10 with 5

Now, to simplify further divide the numbers to get

$\left(-10\right)÷5=-2$