Solve 3² + 3³: Adding Sequential Powers of Three

Exponent Rules with Order of Operations

Sovle:

32+33 3^2+3^3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's solve this problem together.
00:06 First, calculate each power separately, then combine them.
00:11 Remember, a power is a number, multiplied by itself as many times as the exponent says.
00:17 Break down each power into simple multiplications. Let's solve them step by step.
00:24 Solve each multiplication one at a time. Keep going until they are all solved.
00:30 Now, substitute these solutions back into the problem and calculate the final answer.
00:36 And there you have it! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Sovle:

32+33 3^2+3^3

2

Step-by-step solution

Remember that according to the order of operations, exponents precede multiplication and division, which precede addition and subtraction (and parentheses always precede everything).

So first calculate the values of the terms in the power and then subtract between the results:

32+33=9+27=36 3^2+3^3 =9+27=36 Therefore, the correct answer is option B.

3

Final Answer

36

Key Points to Remember

Essential concepts to master this topic
  • Order Rule: Calculate exponents first, then perform addition or subtraction
  • Technique: 32=9 3^2 = 9 and 33=27 3^3 = 27 , then add: 9 + 27
  • Check: Verify each power separately: 3×3=9, 3×3×3=27, final sum=36 ✓

Common Mistakes

Avoid these frequent errors
  • Adding the exponents instead of calculating powers first
    Don't add 2+3=5 and calculate 35=243 3^5 = 243 ! This ignores order of operations and gives a completely wrong answer. Always calculate each exponent separately first, then add the results: 32+33=9+27=36 3^2 + 3^3 = 9 + 27 = 36 .

Practice Quiz

Test your knowledge with interactive questions

\( 11^2= \)

FAQ

Everything you need to know about this question

Why can't I just add the exponents 2 + 3?

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Because 32+33 3^2 + 3^3 means "3 squared plus 3 cubed", not "3 to the power of (2+3)". These are completely different operations! You must calculate each power separately first.

What's the difference between 3² and 3³?

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32=3×3=9 3^2 = 3 \times 3 = 9 (3 multiplied by itself once), while 33=3×3×3=27 3^3 = 3 \times 3 \times 3 = 27 (3 multiplied by itself twice). The exponent tells you how many times to use 3 as a factor.

How do I remember the order of operations?

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Use PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. For this problem, exponents come before addition, so calculate 32 3^2 and 33 3^3 first!

What if I calculated 3² as 6 instead of 9?

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That's a common error! 32 3^2 means 3 times 3, not 3 times 2. The exponent tells you how many 3's to multiply together, not what to multiply 3 by.

Can I use a calculator for this?

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Yes, but enter it correctly! Type 3^2 + 3^3 or use parentheses. Most calculators follow order of operations automatically and will give you 36.

How can I double-check my answer?

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Work backwards: if your answer is 36, break it down. Does 36 = 9 + 27? Yes! Do 9 and 27 equal 32 3^2 and 33 3^3 ? Check: 3×3=9 ✓ and 3×3×3=27 ✓

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