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

\( 6+\sqrt{64}-4= \)

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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