Calculate 8^3: Converting an Exponent to Integer Form

Q: What does the little 3 mean in $ 8^3 $ ?

The little 3 is called an exponent and tells you how many times to use 8 as a factor. So $ 8^3 $ means 8 × 8 × 8, not 8 × 3!

Q: Is there a pattern to help me remember cube values?

Yes! Perfect cubes follow a pattern: $ 1^3 = 1 $, $ 2^3 = 8 $, $ 3^3 = 27 $, $ 4^3 = 64 $, $ 5^3 = 125 $. Notice how each result is much larger than the base!

Q: How do I multiply 64 × 8 without a calculator?

Break it down: 64 × 8 = 64 × (10 - 2) = 640 - 128 = 512. Or think: 64 × 8 = 8 × 8 × 8, and you know 8 × 8 = 64, so it's like counting by 64s eight times.

Q: Why is 512 the right answer and not 215 or 125?

215 is too small (that's closer to $ 6^3 $), and 125 is actually $ 5^3 $. Since 8 > 5, we know $ 8^3 $ must be much larger than 125!

Q: Can I use shortcuts for calculating $ 8^3 $ ?

Yes! Since 8 = $ 2^3 $, you can write $ 8^3 = (2^3)^3 = 2^9 $. Then $ 2^9 = 2^8 \times 2 = 256 \times 2 = 512 $. This confirms our answer!

Exponent Calculations with Perfect Cubes

Write the following as an integer:

$8^3=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's use the power formula

00:06 Any number (X) to the power of (N)

00:09 equals X multiplied by itself N times

00:18 Let's use this formula in our exercise

00:23 Let's break down the power into multiplications

00:35 Let's calculate the multiplications

00:39 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the following as an integer:

$8^3=$

Step-by-step solution

To solve this problem, we need to calculate the value of $8^3$ .

Let's work through the calculation step-by-step:

First, calculate $8 \times 8$ . This gives: $8 \times 8 = 64$ .
Next, we multiply the result by 8 again: $64 \times 8 = 512$ .

Therefore, the value of $8^3$ is 512.

Final Answer

512

Key Points to Remember

Essential concepts to master this topic

Rule: An exponent tells how many times to multiply the base
Technique: Calculate $8^3 = 8 \times 8 \times 8 = 64 \times 8 = 512$
Check: Verify by recognizing 8 is $2^3$ , so $8^3 = (2^3)^3 = 2^9 = 512$ ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying
Don't calculate 8 + 8 + 8 = 24 when you see $8^3$ ! This confuses addition with exponentiation and gives completely wrong results. Always multiply the base by itself the number of times shown by the exponent.

Practice Quiz

Test your knowledge with interactive questions

Which of the following is equivalent to the expression below?

$$ $$ 10,000^1 $$

FAQ

Everything you need to know about this question

What does the little 3 mean in $8^3$ ?

The little 3 is called an exponent and tells you how many times to use 8 as a factor. So $8^3$ means 8 × 8 × 8, not 8 × 3!

Is there a pattern to help me remember cube values?

Yes! Perfect cubes follow a pattern: $1^3 = 1$ , $2^3 = 8$ , $3^3 = 27$ , $4^3 = 64$ , $5^3 = 125$ . Notice how each result is much larger than the base!

How do I multiply 64 × 8 without a calculator?

Break it down: 64 × 8 = 64 × (10 - 2) = 640 - 128 = 512. Or think: 64 × 8 = 8 × 8 × 8, and you know 8 × 8 = 64, so it's like counting by 64s eight times.

Why is 512 the right answer and not 215 or 125?

215 is too small (that's closer to $6^3$ ), and 125 is actually $5^3$ . Since 8 > 5, we know $8^3$ must be much larger than 125!

Can I use shortcuts for calculating $8^3$ ?

Yes! Since 8 = $2^3$ , you can write $8^3 = (2^3)^3 = 2^9$ . Then $2^9 = 2^8 \times 2 = 256 \times 2 = 512$ . This confirms our answer!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Powers and Roots - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Calculate 8^3: Converting an Exponent to Integer Form

Exponent Calculations with Perfect Cubes

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What does the little 3 mean in $8^3$ ?

Is there a pattern to help me remember cube values?

How do I multiply 64 × 8 without a calculator?

Why is 512 the right answer and not 215 or 125?

Can I use shortcuts for calculating $8^3$ ?

🌟 Unlock Your Math Potential

More Questions

Powers

Calculate 6^5: Converting an Exponential Expression to an Integer

Calculate 4 to the Fourth Power: Finding the Value of 4^4

Calculate 10^3: Converting Powers to Integer Form

Calculate 11³: Converting Powers to Integer Form

Calculate 8^3: Converting an Exponent to Integer Form

Exponent Calculations with Perfect Cubes

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What does the little 3 mean in 83 8^3 83?

Is there a pattern to help me remember cube values?

How do I multiply 64 × 8 without a calculator?

Why is 512 the right answer and not 215 or 125?

Can I use shortcuts for calculating 83 8^3 83?

🌟 Unlock Your Math Potential

More Questions

Powers

Calculate 6^5: Converting an Exponential Expression to an Integer

Calculate 4 to the Fourth Power: Finding the Value of 4^4

Calculate 10^3: Converting Powers to Integer Form

Calculate 11³: Converting Powers to Integer Form

What does the little 3 mean in $8^3$ ?

Can I use shortcuts for calculating $8^3$ ?