# How do you evaluate (1 + 3 * 3)^2 + 8?

Mar 20, 2018

108

#### Explanation:

• Remember that PEMDAS:

• List item

• List item
• Parenthesis
• Exponents
• Multiplication
• Division
• Subtraction

*Remember that steps 3/4 can happen in either order depending on what appear first when reading the equation from left to right. This same rule applies with steps 5/6 as well *

is the necessary order of operations to solve all equations.

• Solving the Equation:

${\left(1 + 3 \cdot 3\right)}^{2} + 8$
- to begin, rewrite the problem, and identify the first step according to PEMDAS
- The first letter of PEMDAS, P stands for parenthesis, which are present
- So, we begin by solving inside the parenthesis

${\left(1 + 3 \cdot 3\right)}^{2} + 8$

• Inside the parenthesis, we restart with PEMDAS: Since there are no parenthesis or exponents INSIDE the parenthesis, we move on to multiplication - 3 x 3 = 9 - so the equation should look like this:

${\left(1 + 9\right)}^{2} + 8$

• To finish the parenthesis, we move down PEMDAS - since there is no more multiplication or division, we can add -
• 1 + 9 = 10 - so the parenthesis are removed because they have been simplified, and the equation should look like this:

${10}^{2} + 8$

• Then, we return to the beginning of PEMDAS - since there are no more parenthesis, we can move on to the exponent that is present.
• ${10}^{2} = 100$ - so, the number 100 can fill the place of ${10}^{2}$ in the equation

$100 + 8$

• Finally, we can move on to the next part of PEMDAS - since there is no more multiplication or division, we can move on addition and subtraction

$100 + 8 = 108$ - so you have your answer!