Chapter 1, Problem 1RE

For the following exercises, perform the given operations.

$1.{(5-3\cdot 2)}^2-6$

To determine

To simplify:

the given numerical expression ${\left(5-3\cdot 2\right)}^2-6$.

Explanation of Solution

Given information:

${\left(5-3\cdot 2\right)}^2-6$

Concept Involved:

PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete

Calculation:

Steps	Description   ${\left(5-3\cdot 2\right)}^2-6$
${\left(5-\underset{\_}{3\cdot 2}\right)}^2-6={\left(5-\underset{\_}{6}\right)}^2-6$	We need to perform the operation inside the parenthesis, Multiplying $3\cdot 2$ inside the parenthesis
${\left(\underset{\_}{5-6}\right)}^2-6=\underset{\_}{{\left(-1\right)}^2}-6$	We need to perform the operation inside the parenthesis, Adding $5-6$ inside the parenthesis
$\underset{\_}{{\left(-1\right)}^2}-6=\underset{\_}{1}-6$	We need to perform the exponent, so finding the value of ${\left(-1\right)}^2$
$\underset{\_}{1-6}=\boxed{-5}$	We need to add the numbers to get the final answer

Conclusion:

The value of numerical expression ${\left(5-3\cdot 2\right)}^2-6$is given by: $\boxed{-5}$