Chapter R.11, Problem 1DE

Simplify.

$9\left[8-7\left(5-2\right)\right]$

To determine

To calculate: The simplified form of the expression $9\left[8-7\left(5-2\right)\right]$.

Answer to Problem 1DE

Solution:

The simplified form of the expression $9\left[8-7\left(5-2\right)\right]$ is $\underset{\_}{-117}$.

Explanation of Solution

Given information:

The provided expression is $9\left[8-7\left(5-2\right)\right]$.

Formula Used:

Order of operations:

Step 1: First, simplify the modulus, parenthesis and brackets by solving, first brackets, then multiplication and division from left to right and then subtraction and addition from left to right in the expressions inside them.

Step 2: Secondly, simplify the exponential powers.

Step 3: Then perform multiplication and division from left to right.

Step 4: Finally, perform subtraction and addition from left to right.

Calculation:

Consider the expression,

$9\left[8-7\left(5-2\right)\right]$

Follow the order of operations to solve the above expression.

First, do the calculations in the brackets as below:

$\begin{array}{c}9\left[8-7\left(5-2\right)\right]=9\left[8-7\left(3\right)\right]\\ =9\left[8-7\cdot 3\right]\end{array}$

Perform multiplication from left to right as below;

$\begin{array}{c}9\left[8-7\left(5-2\right)\right]=9\left[8-7\left(3\right)\right]\\ =9\left[8-7\cdot 3\right]\\ =9\left[8-21\right]\end{array}$

Finally, perform subtraction from left to right and further simplify as below;

$\begin{array}{c}9\left[8-7\left(5-2\right)\right]=9\left[8-21\right]\\ =9\cdot \left(-13\right)\\ =-117\end{array}$

Hence, the simplified form of the expression $9\left[8-7\left(5-2\right)\right]$ is $-117$.