Chapter SH, Problem 21SEWI

Solution

To simplify the expression $\left(-3+2^3\right)\left(4+\frac{-42}{7}\right)$ .

  $-10$

Given information:

The expression, $\left(-3+2^3\right)\left(4+\frac{-42}{7}\right)$

Concept used:

For Order of Operation, we will use PEMDAS rule.

Symbols are representing:

P − parenthesis, E − exponent, M − multiplication,

D − division, A − addition and S − subtraction.

• If grouping symbols such as parenthesis are present, simplify expressions within those first, starting with the innermost set.
• Evaluate exponential expressions or absolute values in order from left to right.
• Multiply or divide in order from left to right.
• Add or subtract in order from left to right.

If there are no grouping symbols or no exponents, we multiply or divide and then add or subtract in the order from left to right.

Calculation:

In order to simplify the expression $\left(-3+2^3\right)\left(4+\frac{-42}{7}\right)$ , solve the expression inside the grouping symbol and then simplify further by following the order of operations as shown below

  $\begin{array}{c}\left(-3+2^3\right)\left(4+\frac{-42}{7}\right)=\left(-3+8\right)\left(4+\frac{-42}{7}\right)\\ =\left(-3+8\right)\left(4+\left(-6\right)\right)\\ =\left(5\right)\left(4-6\right)\\ =\left(5\right)\left(-2\right)\\ =-10\end{array}$

Thus, the given expression simplifies to $-10$ .