Solve the Expression: 3×3 + 3² Using Order of Operations

Order of Operations with Mixed Exponents

3×3+32= ? 3\times3+3^2=\text{ ?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve this problem together!
00:09 First, break down the exponent step by step.
00:13 Remember, tackle multiplication and division before moving to addition and subtraction. This helps simplify things.
00:20 And there you have it. That's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

3×3+32= ? 3\times3+3^2=\text{ ?}

2

Step-by-step solution

First we need to remind ourselves of the order of operations:

  1. Parentheses

  2. Exponents and Roots

  3. Multiplication and Division

  4. Addition and Subtraction

There are no parentheses in this problem, therefore we will start with exponents:

3 * 3 + 3² =

3 * 3 + 9 =

Let's continue to the next step—multiplication operations:

3 * 3 + 9 =

9 + 9 =

Finally, we are left with a simple addition exercise:

9 + 9 = 18

3

Final Answer

18

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Always handle exponents before multiplication and addition operations
  • Technique: Calculate 32=9 3^2 = 9 first, then 3×3=9 3 \times 3 = 9 , finally 9+9=18 9 + 9 = 18
  • Check: Verify each step: exponent gives 9, multiplication gives 9, addition gives 18 ✓

Common Mistakes

Avoid these frequent errors
  • Working left to right without following order of operations
    Don't solve 3×3+32 3 \times 3 + 3^2 as (3×3)+32=9+32 (3 \times 3) + 3^2 = 9 + 3^2 then (9+3)2=144 (9 + 3)^2 = 144 ! This ignores PEMDAS and treats addition before exponents. Always handle exponents first, then multiplication, then addition.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

\( 36-4\div2 \)

FAQ

Everything you need to know about this question

Why can't I just work from left to right like in reading?

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Mathematics has a special order called PEMDAS that ensures everyone gets the same answer! Working left to right would give different results depending on how you group operations.

What does the exponent 32 3^2 actually mean?

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32 3^2 means 3 multiplied by itself: 3×3=9 3 \times 3 = 9 . The small 2 tells you how many times to multiply 3 by itself.

How do I remember the order of operations?

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Use the acronym PEMDAS: Please Excuse My Dear Aunt Sally

  • Parentheses
  • Exponents
  • Multiplication and Division (left to right)
  • Addition and Subtraction (left to right)

What if I got 36 as my answer?

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You likely calculated (3×3+3)×3=12×3=36 (3 \times 3 + 3) \times 3 = 12 \times 3 = 36 by mistake. Remember: exponents come before multiplication, so 32=9 3^2 = 9 must be calculated first!

Is there a way to check my work?

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Yes! Work through each step slowly:

  • Step 1: 32=9 3^2 = 9
  • Step 2: 3×3=9 3 \times 3 = 9
  • Step 3: 9+9=18 9 + 9 = 18

If you get 18, you're correct!

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