Solve (15+9÷3-4²)² Using Order of Operations

Q: Why do I have to do the division before addition inside the parentheses?

Even inside parentheses, you still follow PEMDAS order! Parentheses tell you to solve everything inside first, but you still do exponents, then multiplication/division, then addition/subtraction within those parentheses.

Q: What does the colon (:) symbol mean in math?

The colon (:) is another way to write division, just like ÷. So $ 9:3 $ means $ 9 ÷ 3 = 3 $. You'll see this notation in many math problems.

Q: Should I calculate 4² as 4×2 or 4×4?

Always calculate $ 4^2 $ as 4×4=16, not 4×2=8! The exponent tells you how many times to multiply the base by itself. $ 4^2 $ means "4 to the second power" or "4 squared."

Q: How do I avoid making mistakes with the order of operations?

Write out each step clearly and don't skip steps! Use PEMDAS as your guide: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Calculate the exponent

00:06 Always solve multiplication and division before addition and subtraction

00:10 Continue to solve according to the correct order of operations, parentheses first

00:19 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$(15+9:3-4^2)^2=$

2

Step-by-step solution

Let's solve the expression step by step using the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right)).

The expression is: $(15+9:3-4^2)^2$

Start by solving the expression inside the parentheses: $15+9:3-4^2$
Handle the division first: $9:3 = 3$
The expression now becomes $(15+3-4^2)$
Next, handle the exponent: $4^2 = 16$
The expression now becomes $(15+3-16)$
Finally, perform the addition and subtraction from left to right:
$15+3 = 18$
$18-16 = 2$
Now, we need to take this result and square it: $2^2 = 4$

Thus, the final solution to the problem $(15+9:3-4^2)^2$ is: $4$

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then exponents, division/multiplication, addition/subtraction
Technique: Work inside parentheses: 9÷3=3, then 4²=16, then 15+3-16=2
Check: Final answer squared gives reasonable result: 2²=4 ✓

Common Mistakes

Avoid these frequent errors

Computing operations from left to right without following PEMDAS
Don't solve 15+9÷3-4² as (15+9)÷3-4² = 24÷3-16 = 8-16 = -8, then (-8)² = 64! This ignores the order of operations and gives a completely wrong answer. Always follow PEMDAS: handle division and exponents before addition and subtraction.

Practice Quiz

Test your knowledge with interactive questions

$5+\sqrt{36}-1=$

FAQ

Everything you need to know about this question

Why do I have to do the division before addition inside the parentheses?

+

Even inside parentheses, you still follow PEMDAS order! Parentheses tell you to solve everything inside first, but you still do exponents, then multiplication/division, then addition/subtraction within those parentheses.

What does the colon (:) symbol mean in math?

+

The colon (:) is another way to write division, just like ÷. So $9:3$ means $9 ÷ 3 = 3$ . You'll see this notation in many math problems.

Should I calculate 4² as 4×2 or 4×4?

+

Always calculate $4^2$ as 4×4=16, not 4×2=8! The exponent tells you how many times to multiply the base by itself. $4^2$ means "4 to the second power" or "4 squared."

How do I avoid making mistakes with the order of operations?

+

Write out each step clearly and don't skip steps! Use PEMDAS as your guide: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

What if I get a different answer when I check my work?

+

Go back and check each step carefully. Make sure you followed PEMDAS correctly and didn't rush through any calculations. Order of operations mistakes are very common but easy to fix!

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Solve (15+9÷3-4²)² Using Order of Operations

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