Q48. - Algebra 1

Question

Evaluate the expression $7^3-\frac{2}{3}(13\cdot 6+9)4$.

Step-by-Step Solution

Answer

The value of the expression $7^3-\frac{2}{3}(13\cdot 6+9)4$ is 111.

Step 1. Apply the BODMAS rule.

According to the BODMAS rule of simplification, at first, the bracket operation must be completed followed division, by multiplication, addition, and finally subtraction.

Step 2. Example of applying BODMAS rule.

The expression $\frac{{(2+3)}^2}{5(4-3)}$ can be written as

$\begin{array}{l}\frac{{(2+3)}^2}{5(4-3)}=\frac{5^2}{5\left(1\right)}\\ =\frac{5\times 5}{5\times 1}\\ =\frac{25}{5}\\ =5\end{array}$

Step 3. DESCRIPTION OF STEP.

The given expression is $7^3-\frac{2}{3}(13\cdot 6+9)4$

$\begin{array}{l}{7}^3-\frac{2}{3}\left(13\cdot 6+9\right)4\\ \text{Multiply 13 and 6 inside the grouping}\\ 7^3-\frac{2}{3}\left(13\cdot 6+9\right)4=7^3-\frac{2}{3}\left(78+9\right)4\\ \text{Adding 78\& 9 in the grouping}\\ 7^3-\frac{2}{3}\left(13\cdot 6+9\right)4=7^3-\frac{2}{3}\cdot 87\cdot 4\\ \text{Evaluate the power }{7}^3\\ 7^3-\frac{2}{3}\left(13\cdot 6+9\right)4=343-\frac{2}{3}\cdot 87\cdot 4\\ \text{Simplify}\\ 7^3-\frac{2}{3}\left(13\cdot 6+9\right)4=343-2\cdot 29\cdot 4\\ 7^3-\frac{2}{3}\left(13\cdot 6+9\right)4=343-232\\ 7^3-\frac{2}{3}\left(13\cdot 6+9\right)4=111\end{array}$