Calculate 7³: Finding the Cube of Seven

Exponent Calculations with Perfect Cubes

73= 7^3=

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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!
00:07 First, break down the exponent into a series of multiplications.
00:13 Now, calculate each multiplication step by step.
00:17 Use long multiplication to make sure your answer is correct.
00:22 Don't forget to remember the number 3 above. Calculate again and substitute.
00:28 And there you have it, the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

73= 7^3=

2

Step-by-step solution

To solve the problem of finding 73 7^3 , follow these steps:

  • Step 1: Understand that the power 73 7^3 means 7 multiplied by itself three times.
  • Step 2: First, compute 7×7 7 \times 7 . This equals 49.
  • Step 3: Next, multiply the result by 7 again: 49×7 49 \times 7 .
  • Step 4: Calculate 49×7 49 \times 7 , which equals 343.

Therefore, 73=343 7^3 = 343 .

With the possible choices given, the correct answer corresponds to choice 343 343 .

3

Final Answer

343 343

Key Points to Remember

Essential concepts to master this topic
  • Definition: 73 7^3 means multiply 7 by itself three times
  • Technique: Calculate step by step: 7×7=49 7 \times 7 = 49 , then 49×7=343 49 \times 7 = 343
  • Check: Count multiplication steps: 7 appears exactly 3 times in calculation ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of multiplying the base
    Don't calculate 73 7^3 as 7 + 7 + 7 = 21! The exponent tells you how many times to multiply, not add. Always multiply the base by itself: 7×7×7=343 7 \times 7 \times 7 = 343 .

Practice Quiz

Test your knowledge with interactive questions

\( 11^2= \)

FAQ

Everything you need to know about this question

What does the small 3 mean in 73 7^3 ?

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The small 3 is called an exponent. It tells you how many times to use 7 as a factor in multiplication. So 73=7×7×7 7^3 = 7 \times 7 \times 7 .

Why don't I just multiply 7 × 3?

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That would give you 21, which is completely different! The exponent isn't telling you to multiply by 3. It's telling you to use 7 as a factor 3 times in a multiplication problem.

How can I remember what 73 7^3 equals?

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73=343 7^3 = 343 is a perfect cube - a special number worth memorizing! You can remember it by noticing the pattern: 3-4-3, which matches the exponent 3.

What if I got 2401 as my answer?

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You probably calculated 74 7^4 instead! That's 7×7×7×7=2401 7 \times 7 \times 7 \times 7 = 2401 . Always count your multiplication steps carefully to match the exponent.

Is there a faster way than multiplying step by step?

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For small exponents like 3, step-by-step is actually fastest and most reliable. As you practice, you'll memorize common cubes like 23=8 2^3 = 8 , 33=27 3^3 = 27 , and 73=343 7^3 = 343 .

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