Evaluate operations inside grouping symbols such as parentheses (...) or absolute value |...|.
Evaluate exponents such as squares, or cubes.
Evaluate multiplication and division going from left to right.
Evaluate addition and subtraction going from left to right.

PEMDAS is a common acronym that can help us remember the order:

P - parentheses or grouping symbols

E - exponents

M - multiply (we multiply and divide from left to right)

D - divide

A - add (then we add and subtract from left to right)

S - subtract

Let's look at the following example on how to evaluate expressions with whole number exponents.

Evaluate 2^5\times 2^4.

Worked Solution

Create a strategy

Express the product of 2^5 and 2^4 in expanded notation.

Remember:

Apply the idea

Note that the power tells you how many times the base is multiplied by itself.

\displaystyle 2^5\times 2^4	\displaystyle =	\displaystyle (2\times 2 \times 2 \times 2 \times 2) \times (2 \times 2 \times 2 \times 2 )
	\displaystyle =	\displaystyle 2\times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2
	\displaystyle =	\displaystyle 512

Reflect and check

We can see that:

\displaystyle 2^5\times 2^4	\displaystyle =	\displaystyle 2\times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2
\displaystyle 2^5\times 2^4	\displaystyle =	\displaystyle 2^9

Evaluate the following expression:

6^2 -28\div 4 + 3 \times (7+2)

Worked Solution

Create a strategy

Use the order of operations to decide which operation to perform first.

Apply the idea

\displaystyle 6^2 -28\div 4 + 3 \times (7+2)	\displaystyle =	\displaystyle 6^2 -28\div 4 + 3 \times 9	Evaluate addition inside the parentheses
	\displaystyle =	\displaystyle 36 -28\div 4 + 3 \times 9	Evaluate exponents
	\displaystyle =	\displaystyle 36 -7 + 3 \times 9	Evaluate division
	\displaystyle =	\displaystyle 36 -7 + 27	Evaluate multiplication
	\displaystyle =	\displaystyle 29 + 27	Evaluate subtraction
	\displaystyle =	\displaystyle 56	Evaluate addition

Idea summary

We use order of operations to evaluate expresion with more than two operations.

Evaluate operations inside grouping symbols such as parentheses (...) or absolute value |...|.
Evaluate exponents such as squares, or cubes.
Evaluate multiplication and division going from left to right.
Evaluate addition and subtraction going from left to right.

5.01 Evaluate expressions

Ideas