Calculate 4 Cubed: Finding the Value of 4³

Exponent Operations with Base Numbers

43= 4^3=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Break down from exponent to multiplication
00:09 Break down 16 into 10 plus 6 and multiply
00:12 Multiply by each factor
00:17 Calculate the products
00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

43= 4^3=

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Apply the definition of powers to calculate 434^3.
  • Step 2: Multiply 4 by itself to find intermediate results.
  • Step 3: Verify the calculation against the given choices.

Now, let's work through each step:

Step 1: We need to calculate 434^3, which means multiplying 4 by itself a total of three times.

Step 2: First, calculate 4×4=164 \times 4 = 16. Then, multiply this result by 4 again: 16×4=6416 \times 4 = 64.

Step 3: The final result is 6464, which matches option 1 in the provided choices.

Therefore, the solution to the problem is 6464.

3

Final Answer

64 64

Key Points to Remember

Essential concepts to master this topic
  • Definition: An exponent shows how many times to multiply the base
  • Technique: Calculate 43 4^3 as 4 × 4 = 16, then 16 × 4 = 64
  • Check: Verify by counting: 4 appears 3 times in multiplication 4 × 4 × 4 = 64 ✓

Common Mistakes

Avoid these frequent errors
  • Adding the base and exponent instead of multiplying
    Don't calculate 43 4^3 as 4 + 3 = 7 or 4 × 3 = 12! The exponent tells you how many times to use the base in multiplication, not addition. Always multiply the base by itself the number of times shown by the exponent.

Practice Quiz

Test your knowledge with interactive questions

\( 11^2= \)

FAQ

Everything you need to know about this question

What does the little 3 mean in 43 4^3 ?

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The little 3 is called an exponent or power. It tells you to multiply 4 by itself 3 times: 4×4×4 4 \times 4 \times 4 .

Is there a faster way to calculate 43 4^3 ?

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You can break it down step by step: first calculate 42=16 4^2 = 16 , then multiply by 4 one more time: 16×4=64 16 \times 4 = 64 . This makes big exponents easier!

Why isn't 43 4^3 equal to 12?

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That's a common mistake! 43 4^3 means multiply 4 by itself 3 times, not multiply 4 times 3. Remember: exponents mean repeated multiplication, not regular multiplication.

How do I remember what cubed means?

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Think of a cube shape! A cube has 3 dimensions, so "cubed" means the exponent is 3. 43 4^3 is "4 cubed" and equals 64.

What if I get confused with the order of operations?

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Calculate the exponent first before doing any other operations. In 2+43 2 + 4^3 , you'd calculate 43=64 4^3 = 64 first, then add: 2+64=66 2 + 64 = 66 .

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