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

May 10, 2016

third operation: ${4}^{2} = 16$
fourth operation: $13 \times 16 = 208$

Explanation:

Given $\left[\left(8 + 5\right) {\left(6 - 2\right)}^{2}\right] - \left(4 \cdot \frac{17}{2}\right)$

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.

$\textcolor{w h i t e}{\text{XXX}} \left[\left(8 + 5\right) {\left(6 - 2\right)}^{2}\right]$
and again we have two parenthetical expressions
color(white)("XXX")(8+5)" "and" "(6-2)
and evaluate from left to right.

First $\left(8 + 5\right) = 13$
leaving $\left[13 {\left(6 - 2\right)}^{2}\right]$

Second $\left(6 - 2\right) = 4$
leaving $\left[13 \cdot {4}^{2}\right]$

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 $\left[13 \cdot 16\right]$

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

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

Jul 31, 2016

$174$

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.

$\textcolor{b l u e}{\left[\left(8 + 5\right) {\left(6 - 2\right)}^{2}\right]} \textcolor{m a \ge n t a}{- \left(4 \cdot \frac{17}{2}\right)} \text{ has 2 terms}$

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

=$\textcolor{b l u e}{13 \times \left(16\right)} \textcolor{m a \ge n t a}{- 34}$

=$\textcolor{b l u e}{208} - \textcolor{m a \ge n t a}{34}$

=$174$