Chapter 1.4, Problem 1P

To determine

To Evaluate: The expression $7^3-\frac{2}{3}\left(13\cdot 6+9\right)4$

Answer to Problem 1P

  $7^3-\frac{2}{3}\left(13\cdot 6+9\right)4=111$

Explanation of Solution

Given information:

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

Concept and Formula Used:

Rule of exponent and addition and subtraction.

  $a^n=a\times a\times a\times \mathrm{..................}n\text{ times}\text{.}$

BODMAS rule

Calculation:

The given expression is

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

Conclusion:

  $7^3-\frac{2}{3}\left(13\cdot 6+9\right)4=111$