Q9. - Algebra 1

Question

Evaluate each expression.

$\frac{{\left(4\cdot 3\right)}^2}{9+3}$

Step-by-Step Solution

Answer

The value of the expression $\frac{{\left(4\cdot 3\right)}^{\mathbf{2}}}{\mathbf{9}\mathbf{+}\mathbf{3}}$ is 12.

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 in the numerator.

$\frac{{\left(4\cdot 3\right)}^2}{9+3}=\frac{{\left(12\right)}^2}{9+3}$

Step 3. Evaluate the power

As per the order of operations, evaluate the power in the numerator.

$\frac{{\left(4\cdot 3\right)}^2}{9+3}=\frac{144}{9+3}$

Step 4. Apply addition operation.

Add 9 and 3 in the denominator and simplify the expression.

$\begin{array}{l}\frac{{\left(4\cdot 3\right)}^2}{9+3}=\frac{144}{12}\\ =12\end{array}$

Therefore, the expression is equal to 12.