Question

In the following expression, what are the third and fourth operations?: `[(8+5) (6-2) ^2] - (4*17/2)`

Answer 1

third operation: `4^2=16`
fourth operation: `13xx16=208`

Explanation:

Given `[(8+5)(6-2)^2]-(4*17/2)`

Using PEDMAS
To begin we must evaluate everything inside parentheses.
At the top level we have two parenthetical expressions:
`color(white)("XXX")[(8+5)(6-2)^2]" "and" "(4*17/2)`
In this case we work from left to right.

So we start with
`color(white)("XXX")[(8+5)(6-2)^2]`
and again we have two parenthetical expressions
`color(white)("XXX")(8+5)" "and" "(6-2)`
and evaluate from left to right.

First `(8+5)=13`
leaving `[13(6-2)^2]`

Second `(6-2)=4`
leaving `[13*4^2]`

There are no more parentheses within the initial square brackets,
so according to P E DMAS the next step is E: exponentiation.
Third operation `4^2=16`
leaving `[13 * 16]`

Next according to PE DM AS is D ivision and M ultiplication (left-to-right)
Fourth operation `[13 * 16]=208`

This completes evaluation of the first set of parenthesized operations and we can move on to evaluating the second set.

Answer 2

`174`

Explanation:

It is difficult to number the operations......

Count the number of terms first. There can be more than one calculation in each step as long as they are within each term and the stronger operations are done before the weaker ones.

Parentheses are done first.

`color(blue)([(8+5)(6-2)^2])color(magenta)(-(4*17/2))" has 2 terms"`

=`color(blue)([(13)xx(4)^2])color(magenta)(-((cancel4^2xx17)/cancel2)`

=`color(blue)(13xx(16))color(magenta)(-34)`

=`color(blue)(208) - color(magenta)(34)`

=`174`