Question

Evaluate each expression.

$108÷\left[3\left(9+3^2\right)\right]$

Short answer

The value of the expression $\mathbf{108}\mathbf{÷}\left[3\left(9+3^2\right)\right]$is 2.

Step-by-step solution

Step 1. Order of operations.

In order to evaluate an expression, the order of operations must be followed, which is:

1. Evaluate the expressions inside the bracket
2. Evaluate the powers
3. Multiply and/or divide
4. Add and/ or subtract

The evaluation takes place from left to right.

Step 2. Evaluate the expression inside the bracket.

In order to evaluate the expression inside the bracket, first, evaluate the innermost expression .

$\begin{array}{l}108÷\left[3\left(9+3^2\right)\right]=108÷\left[3\left(9+9\right)\right]\\ =108÷\left[3\left(18\right)\right]\\ =108÷\left[54\right]\\ =108÷54\end{array}$

Step 3. Divide 108 by 54.

As per the order of operations, now apply the division operation.

$\begin{array}{l}108÷\left[3\left(9+3^2\right)\right]=108÷54\\ =2\end{array}$

Therefore, the expression is equal to 2.