Order of Operations with Exponents

Order of operations is 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.

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 \(brackets\,  [ \,]\), \(parentheses\, (\,)\), \(braces \left \{ \right \}\), and \(fraction\, bars\).

Then, evaluate exponents and roots of numbers (for example, square roots).

Then, apply multiplication and division, from left to right.

Then add and subtract, also from left to 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 \(14 + 28 \div 2^{2}\)

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

  1. First, simplify \(2^{2}\)
  2. Then, perform division before addition: \(14 + 28 \div 4\)
  3. Then, add, to end up with \(21\).

In summary

Order of Operations provides 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.

1. Simplify.

\((10 - 8)^{2} - (7 -5)^{3}\)
A.
B.
C.
D.

Question 1 of 2

2. Simplify:

\(-4 + 5(-4)^{3}\)
A.
B.
C.
D.

Question 2 of 2


 

Next Lesson: Language of Algebra

 

Last Updated on January 5, 2021.

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