BEDMAS with exponents

BEDMAS with exponents

This lesson will focus on BEDMAS with exponents thrown in the mix!

Order of operations

Math is done in a specific way. We can use the acronym BEDMAS to help us remember the order in which we solve problems.

BEDMAS

B - Brackets

E - Exponents

D - Division

M - Multiplication

A - Addition

S - Subtraction

What does this mean?

We can follow these steps to solve complex looking math problems!

1. Simplify anything inside brackets

2. Simplify any exponents

3. Do all the division and multiplication from left to right

4. Do all the addition and subtraction from left to right

Example

 $2^3+1$  

There are no brackets, so we move on to exponents:

 $2^3=2\times2\times2=8$  

Therefore  $2^3+1=8+1=9$  

Another example

 $8-3^2$  

Again, we don't have any brackets so we simplify the exponents

 $3^2=3\times3=9$  

We don't have any multiplying or dividing, so we finish by subtracting

 $8-3^2=8-9=-1$  

One more example

  $\left(3-1\right)^3$  

In this case, we have brackets so we have to simplify those first

 $3-1=2$  

Now we can apply the exponent:

 $\left(3-1\right)^3=2^3=2\times2\times2=8$  

Try the next 4 questions on your own!

Multiple Choice

What is

 $4^2+3$  

• 7

• 11

• 15

• 19

Multiple Choice

What is

 $5^2-2^2$  

• 6

• 15

• 21

• 29

Multiple Choice

What is

 $\left(2+1\right)^2$  

• 3

• 5

• 7

• 9

Multiple Choice

What is

 $\left(5-6\right)^4$  

• 1

• -1

• 4

• -4

Getting more complicated...

 $\left[2\times\left(-2\right)^3\right]^2$  

In this example, we have multiple exponents and brackets as well!

First we need to simplify the brackets. Inside the brackets, there is multiplication and an exponent.

BEDMAS says we need to simplify the exponent first:
 $\left(-2\right)^3=\left(-2\right)\times\left(-2\right)\times\left(-2\right)=-8$  

Getting more complicated...

 $\left[2\times\left(-2\right)^3\right]^2$  

 $\left(-2\right)^3=\left(-2\right)\times\left(-2\right)\times\left(-2\right)=-8$  

Now we can multiply that by the 2 to finish simplifying our bracket:

 $\left[2\times\left(-2\right)^3\right]^2\ =\ \left[2\times\left(-8\right)\right]^2=\left(-16\right)^2$  

Getting more complicated...

 $\left[2\times\left(-2\right)^3\right]^2\ =\ \left[2\times\left(-8\right)\right]^2=\left(-16\right)^2$  

Now we can finish by simplifying the last exponent:

 $\left(-16\right)^2=256$  

Another example

 $\left(7^2+5^0\right)\div\left(-5\right)^1$  

First we simplify brackets. Inside the brackets, we have exponents that need to be simplified before we can add them together:

 $7^2=7\times7=49$  and  $5^0=1$  , so

 $\left(7^2+5^0\right)=\left(49+1\right)=50$  

Another example

 $\left(7^2+5^0\right)\div\left(-5\right)^1$  

Next we simplify our exponent:

 $\left(-5\right)^1=\left(-5\right)$  

Another example

 $\left(7^2+5^0\right)\div\left(-5\right)^1$  

Now we can do the division in the middle:

 $\left(7^2+5^0\right)\div\left(-5\right)^1=50\div\left(-5\right)=-10$  

Remember, when we divide a positive number by a negative number, our answer will be negative.

Try the next 2 questions on your own!

Multiple Choice

What is

 $8^2\div4$  

• 4

• 8

• 12

• 16

Multiple Choice

What is

 $\left(3^2+6^0\right)\div2^1$  

• 3

• 4

• 5

• 6

Why should we care about BEDMAS?

The answer... SKILL TESTING QUESTIONS!

In Canada, in order to win a prize, we need to answer a skill testing question before we can receive the prize. Normally, these questions are solved using BEDMAS!

Some examples

This is an example for a Roll Up the Rim skill testing question

Skill testing question example

You won a $100 Gift Card from Tim's in Roll Up the Rim! Answer the skill testing question to claim your prize!

 $400\div4^2+2^{ }\times80$  

Multiple Choice

What do we do first?

• $400\div4$

• $4^2$

• $2\times80$

• $4+2$

Skill testing question example

We do:

 $4^2$ first, which equals 16.

Now we have:

  $400\div16+2\times80$  

Multiple Choice

What do we do next?

• $400\div16$

• $16+2$

• $2\times80$

Skill testing question example

We can do the division and the multiplication next.

 $400\div16=25$  and  $2\times80=160$  

Skill testing question example

We finish by adding the two answers together:

 $25+160=185$  

PRACTICE

Practice the following questions about BEDMAS!

Multiple Choice

What does the B in BEDMAS stand for?

• Brackets

• Beavers

• Boom Boom

• Binoculars

Multiple Choice

What does the E in BEDMAS stand for?

• Eagle

• Exponents

• Excellent

• Elementary

Multiple Choice

We can do division and multiplication in the same step, from left to right.

• True

• False

Multiple Choice

What do we do first in the following equation?

 $100\div\left(2+3\right)^2-17\times32$  

• 100

• 2 + 3

• -17

• 17 x 32

Multiple Choice

What do we do first in the following equation?

 $100÷2+3^2−17×32$  

•  $100\div2$  

•  $17\times32$  

•  $3^2$  

•  $-17$  

Multiple Choice

Solve this equation using BEDMAS:

5 x (3 + 2)

• 17

• 25

• 30

• 42

Multiple Choice

Solve the equation using BEDMAS:

8 + 2 x 6

• 8

• 10

• 20

• 60

Multiple Choice

Solve this equation using BEDMAS:

 $\left(3\div1\right)^2$  

• 27

• 9

• 3 

• 1

Multiple Choice

Solve this equation:

 $2^3-1$  

• 5

• 7

• 9

• 11

Multiple Choice

Solve this equation:

 $\left(7^2+1\right)\div\left(2^3+2\right)$  

• 3

• 5

• 6

• 8