Calculate 11³: Converting Powers to Integer Form

Q: What does the small 3 above the 11 mean?

The small number 3 is called an exponent. It tells you to multiply 11 by itself 3 times: $ 11 \times 11 \times 11 $.

Q: Why don't I just multiply 11 × 3?

Exponents are different from multiplication! $ 11^3 $ means repeated multiplication of 11, not $ 11 \times 3 = 33 $. Remember: exponent = repeated multiplication.

Q: How can I remember what 11³ equals?

Try this pattern: $ 11^2 = 121 $ and $ 11^3 = 1331 $. Notice how the digits are symmetric (read the same forwards and backwards)!

Q: What if I get a different answer when I check my work?

Double-check your multiplication! Start over with $ 11 \times 11 $, then carefully multiply that result by 11 again. Take your time with each step.

Exponent Calculation with Base Eleven

Write the following as an integer:

$11^3=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We'll use the power formula

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

00:09 equals X multiplied by itself N times

00:21 We'll use this formula in our exercise

00:26 We'll break down the power into multiplications

00:39 We'll calculate the multiplications

00:46 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:

$11^3=$

Step-by-step solution

To solve this problem, we'll multiply as follows:

Step 1: Compute $11 \times 11 = 121$ .
Step 2: Take the result from Step 1 and multiply it by 11 again: $121 \times 11$ .

Let's perform the multiplication for Step 2:

To calculate $121 \times 11$ , we can use a standard multiplication method:

121
×11
----
From the rightmost digit: $1 \times 1 = 1$ .
Next: $1 \times 2 = 2$ . Add the carried over part (none here, so just 2).
Finally: $1 \times 1 = 1$ .

Thus, the basic multiplication gives us 121. Now multiply by 10 (shift left):

Shifted 121 becomes 1210 (since it represents $121 \times 10$ ).
Add these values:
121
+1210
-----
1331

Therefore, the solution to $11^3$ is 1331.

Final Answer

1331

Key Points to Remember

Essential concepts to master this topic

Definition: $11^3$ means multiply 11 by itself three times
Method: Calculate $11 \times 11 = 121$ , then $121 \times 11$
Check: Verify $1331 ÷ 11 ÷ 11 = 11$ to confirm answer ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying
Don't calculate $11^3$ as 11 + 11 + 11 = 33! This confuses exponents with multiplication. An exponent tells you how many times to multiply the base by itself. Always multiply: $11 \times 11 \times 11 = 1331$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

What does the small 3 above the 11 mean?

The small number 3 is called an exponent. It tells you to multiply 11 by itself 3 times: $11 \times 11 \times 11$ .

Why don't I just multiply 11 × 3?

Exponents are different from multiplication! $11^3$ means repeated multiplication of 11, not $11 \times 3 = 33$ . Remember: exponent = repeated multiplication.

Is there a faster way than multiplying step by step?

For small exponents like 3, step-by-step is usually fastest and most reliable. As you advance, you'll learn shortcuts, but mastering the basic method first is essential!

How can I remember what 11³ equals?

Try this pattern: $11^2 = 121$ and $11^3 = 1331$ . Notice how the digits are symmetric (read the same forwards and backwards)!

What if I get a different answer when I check my work?

Double-check your multiplication! Start over with $11 \times 11$ , then carefully multiply that result by 11 again. Take your time with each step.

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