Calculate 12^5: Converting Power to Integer Result

Q: Is there a faster way to calculate large exponents like this?

Yes! You can use the sequential multiplication method shown in the solution. Calculate $ 12^2 $ first, then use that result to find $ 12^3 $, and so on. This reduces errors compared to multiplying all at once.

Q: What if I make an arithmetic error in the middle steps?

Double-check each multiplication! If you get $ 12^2 = 144 $ wrong, every subsequent step will be incorrect. Take your time with each calculation.

Q: Why not just memorize that 12^5 = 248832?

Understanding the process is more valuable than memorizing! You'll encounter many different bases and exponents, so knowing how to calculate any power systematically is much more useful.

Exponent Calculation with Sequential Multiplication

Write the following as an integer:

$12^5=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Alright class, let's solve this problem together.

00:09 We'll use a power formula to help us out.

00:12 So, any number X raised to the power of N means.

00:17 X multiplied by itself, N times. Let's remember this.

00:25 We'll apply this formula in our exercise here.

00:30 Step by step, we'll break the power into simple multiplications.

00:44 Next, we'll carefully calculate each multiplication.

00:59 And there you have it! That is the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the following as an integer:

$12^5=$

Step-by-step solution

To solve this problem, we'll perform repeated multiplication to find $12^5$ , as follows:

Step 1: Compute $12^2 = 12 \times 12 = 144$ .
Step 2: Compute $12^3 = 144 \times 12 = 1728$ .
Step 3: Compute $12^4 = 1728 \times 12 = 20736$ .
Step 4: Finally, compute $12^5 = 20736 \times 12 = 248832$ .

Through these calculations, we determined that the value of $12^5$ is $248832$ .

Therefore, the solution to the problem is $248832$ and this corresponds to choice 3.

Final Answer

248832

Key Points to Remember

Essential concepts to master this topic

Rule: Build powers step by step using previous results
Technique: Calculate $12^2 = 144$ , then $144 \times 12 = 1728$
Check: Verify by calculating differently: $12^5 = 12 \times 12 \times 12 \times 12 \times 12 = 248832$ ✓

Common Mistakes

Avoid these frequent errors

Calculating 12 × 5 instead of exponential form
Don't confuse $12^5$ with 12 × 5 = 60! The exponent means multiply 12 by itself 5 times, not multiply 12 by 5. Always remember that $a^n$ means 'a' multiplied by itself 'n' times.

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

Is there a faster way to calculate large exponents like this?

Yes! You can use the sequential multiplication method shown in the solution. Calculate $12^2$ first, then use that result to find $12^3$ , and so on. This reduces errors compared to multiplying all at once.

Can I use a calculator for this problem?

While calculators can help verify your answer, it's important to understand the process. Try working through the steps manually first, then use a calculator to check your work!

What if I make an arithmetic error in the middle steps?

Double-check each multiplication! If you get $12^2 = 144$ wrong, every subsequent step will be incorrect. Take your time with each calculation.

How do I know which answer choice is correct?

Work through the calculation step by step as shown. The correct answer is 248832. The other choices are common wrong answers from calculation errors or misunderstanding exponents.

Why not just memorize that 12^5 = 248832?

Understanding the process is more valuable than memorizing! You'll encounter many different bases and exponents, so knowing how to calculate any power systematically is much more useful.

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