Step by step
Start inside the first parentheses
Mr DJ begins with 24 ÷ 2 because it's inside the parentheses. That gives 12, so the first group now reads (12 − 7). He brings everything else down, including the 5² in front.
▶ Watch this step 0:13Do the exponent inside the second parentheses
In (2² + 6), the exponent comes before the addition, so 2² = 4. The group now reads (4 + 6), with its square still waiting outside.
▶ Watch this step 0:27Finish both sets of parentheses
There are still parentheses to resolve: 12 − 7 = 5 and 4 + 6 = 10. Once each group is a single number, you can drop the parentheses, so the problem is 5² ÷ 5 + 10².
▶ Watch this step 0:35Work out the exponents
Now do the exponents: 5² = 25 and 10² = 100. That leaves 25 ÷ 5 + 100.
▶ Watch this step 0:56Divide, then add
Division comes before addition, so 25 ÷ 5 = 5. Last, 5 + 100 = 105.
▶ Watch this step 1:23
“First, let's do 24 ÷ 2 because it's in the parentheses.”
Worked example · with Pi the Owl
Try one more, step by step
Problem: 6² ÷ (20 ÷ 2 − 6) + (2² + 1)²
- First parentheses: 20 ÷ 2 = 10, so the group is (10 − 6)
- Second parentheses: 2² = 4, so the group is (4 + 1)
- Finish the parentheses: 10 − 6 = 4 and 4 + 1 = 5, giving 6² ÷ 4 + 5²
- Exponents: 6² = 36 and 5² = 25, giving 36 ÷ 4 + 25
- Divide: 36 ÷ 4 = 9, giving 9 + 25
- Add: 9 + 25 = 34
Answer: 34
Check: Work the second parentheses before the first and you still get 34, because the two groups don't affect each other.
Common mistakes
- Squaring each part of (2² + 6)² separately: 4² + 6² = 16 + 36 = 52. Finish the inside first so it's one number, 4 + 6 = 10, then square it: 10² = 100.
- Subtracting first inside (24 ÷ 2 − 7) because it's in parentheses. PEMDAS still applies inside the parentheses: 24 ÷ 2 = 12 first, then 12 − 7 = 5.
- Reading 5² as 5 × 2 = 10. 5² means 5 × 5 = 25.
- Adding before dividing at the end, as if it were 25 ÷ (5 + 100). Division comes before addition: 25 ÷ 5 = 5, then 5 + 100 = 105.
Questions
What is 5² ÷ (24 ÷ 2 − 7) + (2² + 6)²?
It equals 105. The parentheses become 12 − 7 = 5 and 4 + 6 = 10, so the problem is 5² ÷ 5 + 10² = 25 ÷ 5 + 100 = 5 + 100 = 105.
Do you do exponents inside parentheses first?
Yes. Everything inside the parentheses comes first, in PEMDAS order, so 2² = 4 before you add 6. The exponent outside waits until the inside is one number: (4 + 6)² = 10² = 100.
Read the full transcript
0:00 Order of Operations PEMDAS in under 2 minutes. Let's get going. Just know right away before we get started PEMDAS parentheses exponents multiplication division addition and subtraction. All right, let's go. First, let's do 24 / 2 because it's in the parentheses. That's going to get us 12 right here. Bring down the minus 7 parentheses. Let's put the 5 to the second here. Plus all right, let's do inside these parentheses. Let's do 2 squared which is going to get us 4 right there and we still have plus 6 and squared right there. Now we still have parentheses that we have to resolve here. So let's do 12 minus 7. That gets us 5 right there. We still have the divided
0:46 by sign. We still have 5 squared right there. Plus and 4 plus 6 is 10 and we still have that squared right there. Okay. Now let's do 5 squared right here and that's going to get us 25 and divided by that 5. We can drop those parentheses at this point 10 squared. Okay, let's do 10 squared. That gets us 100 plus we have 5 right here divided by and 25. 25 / 5 25 / 5 is 5 plus 100
1:33 and then we have plus 100. 5 plus 100 that gets us boom right here. Run out of space 105 under 2 minutes. Let's go.
From the video’s captions.
