Calculate 3² - 3³: Evaluating the Difference Between Powers

Order of Operations with Negative Results

What is the answer to the following?

32−33 3^2-3^3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this math problem together.
00:08 First, calculate each power separately, then subtract.
00:12 Remember, a power means multiplying a number by itself, based on the exponent.
00:18 Break the powers into multiplication steps and solve each step carefully.
00:23 Tackle one multiplication at a time. Keep going step by step!
00:29 Now, plug these solutions back into the problem and solve.
00:33 Great job! That's the solution. Keep practicing!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the answer to the following?

32−33 3^2-3^3

2

Step-by-step solution

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

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

32−33=9−27=−18 3^2-3^3 =9-27=-18 Therefore, the correct answer is option A.

3

Final Answer

−18 -18

Key Points to Remember

Essential concepts to master this topic
  • Rule: Calculate exponents first, then perform subtraction operations
  • Technique: Evaluate 32=9 3^2 = 9 and 33=27 3^3 = 27 , then subtract: 9 - 27
  • Check: Final answer should be negative since 33>32 3^3 > 3^2 , giving us -18 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting exponents instead of calculating powers first
    Don't subtract the exponents like 32−3=3−1 3^{2-3} = 3^{-1} = wrong approach! This mixes up exponent rules with order of operations. Always calculate each power separately first: 32=9 3^2 = 9 and 33=27 3^3 = 27 , then subtract the results.

Practice Quiz

Test your knowledge with interactive questions

\( 11^2= \)

FAQ

Everything you need to know about this question

Why do I calculate the exponents before subtracting?

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The order of operations (PEMDAS/BODMAS) tells us that exponents come before addition and subtraction. So you must calculate 32 3^2 and 33 3^3 first, then subtract the results!

How do I remember what 32 3^2 and 33 3^3 equal?

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32 3^2 means 3 × 3 = 9, and 33 3^3 means 3 × 3 × 3 = 27. The exponent tells you how many times to multiply the base by itself.

Why is the answer negative?

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Since 33=27 3^3 = 27 is larger than 32=9 3^2 = 9 , when we subtract we get 9 - 27 = -18. Always pay attention to which number is larger!

Can I use a calculator for this?

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Yes! But make sure to enter it correctly: press 3, ^, 2, -, 3, ^, 3. Most calculators follow order of operations automatically and will give you -18.

What if I accidentally got a positive answer?

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You probably calculated 33−32=27−9=18 3^3 - 3^2 = 27 - 9 = 18 instead. Double-check the order in the original problem: it's 32−33 3^2 - 3^3 , not the other way around!

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