### Numbers: Powers and roots

### Order of operations with powers and roots

We have already seen the order of operations for addition, subtraction, multiplication and division. Now we will look at where powers and roots fit in this order.

Order of operations

When we have an expression that contains multiple operations, we adhere to the following order.

- Perform calculations that are between parentheses.
- Calculate powers and roots.
- Multiply and divide from left to right.
- Add and subtract from left to right.

**Example**

\[\begin{array}{rcl}\sqrt{16}-\left(2+5\right) \times 2^2 &=& \sqrt{16}-7\times 2^2\\&=&4-7\times 4 \\&=&4-28 \\ &=& -24 \end{array}\]

#6 \times {4}^{2}=# # 96#

#\begin{array}{rcl}

6 \times {4}^{2}&=&6 \times (4 \times 4) \\

&&\phantom{xx}\blue{\text{exponentiation is repeated multiplication}}\\

&=&6 \times 16 \\

&&\phantom{xx}\blue{\text{calculated the expression within parentheses}}\\

&=& 96 \\

&&\phantom{xx}\blue{\text{multiplied}}\\

\end{array}#

#\begin{array}{rcl}

6 \times {4}^{2}&=&6 \times (4 \times 4) \\

&&\phantom{xx}\blue{\text{exponentiation is repeated multiplication}}\\

&=&6 \times 16 \\

&&\phantom{xx}\blue{\text{calculated the expression within parentheses}}\\

&=& 96 \\

&&\phantom{xx}\blue{\text{multiplied}}\\

\end{array}#

Unlock full access

Teacher access

Request a demo account. We will help you get started with our digital learning environment.

Student access

Is your university not a partner?
Get access to our courses via

Or visit omptest.org if jou are taking an OMPT exam.

**Pass Your Math**independent of your university. See pricing and more.Or visit omptest.org if jou are taking an OMPT exam.