Order of Operations with Exponents

Order of operations are those rules that are determining the sequence of calculations in expressions that have more than one (1) type of computation.

This lesson explains the Order of Operations when we deal with exponents & square roots.


Question 1 of 2

1. Simplify: 14 + 3 · 42


Question 1 of 2

Question 2 of 2

2. Simplify: 3(2 + 3 · 4)2 − 11.


Question 2 of 2


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The following transcript is provided for your convenience.

The rules of “Order of Operations” allow us to simplify problems that include multiplication, division, addition, and subtraction, or grouping symbols.

What will happens if a problem includes exponents or square roots? We have to expand our rules regarding “Order of Operations” to include exponents and square roots.

First, perform all operations within grouping symbols. Grouping symbols are including brackets [ ], parentheses ( ), braces { }, and fraction bars.
Then, evaluate exponents and roots of numbers (for example square roots).
Then, apply multiplication and division, from the left to the right.
Then add and subtract, also from the left to the right.

If our expression includes exponents or square roots, they may be performed only after parentheses or other grouping symbols are simplified yet before multiplication, division, subtraction, or addition is done that’s outside of the parentheses or some other grouping symbol set.

Example: simplify 14 + 28 ÷ 22

This expression includes addition, division, and has an exponent. Use our order of operations.

First, simplify 22
Then, perform division before addition: 14 + 28 ÷ 4
28/4 = 7
Then, add, to end up with 21.

In summary

Our “Order of Operations” is providing us with a consistent sequence to be used in computations. Without our order of operations, we could end up with totally different answers to exactly identical computation problems.

The Order of Operations and the use of a calculator: Well, there are some cheaper calculators, that are NOT using our order of operations.

When you use these calculators, you must input your numbers in exactly the correct order.

Modern-day calculators will be implementing the correct order of operations, also without your input.

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