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

Q: What does the small number 4 on top mean?

The small number is called an exponent. It tells you how many times to multiply the base number by itself. So $ 4^4 $ means multiply 4 by itself 4 times.

Q: Why can't I just multiply 4 × 4 to get 16?

That would only be $ 4^2 $! For $ 4^4 $, you need to keep multiplying: 4 × 4 × 4 × 4. Count carefully - there should be exactly 4 fours being multiplied together.

Q: How do I know if 256 is the right answer?

You can work backwards! Try to think: what number times 4 equals 256? It's 64. What times 4 equals 64? It's 16. What times 4 equals 16? It's 4. Perfect!

Q: What if I get confused about how many times to multiply?

Write it out the long way first: $ 4^4 = 4 \times 4 \times 4 \times 4 $. Count the fours - there should be exactly 4 of them. Then multiply from left to right, two at a time.

Exponent Calculations with Repeated Multiplication

Write the following as an integer:

$4^4=$

❤️ 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

00:05 Let's solve a math problem together.

00:08 We will use an important math rule called the power formula.

00:13 If you have a number, X, and raise it to the power of N

00:17 it means you multiply X by itself, N times.

00:26 Let's apply this formula to our exercise.

00:30 We'll break down the power into simple multiplications.

00:45 Now, let's perform the calculations step by step.

00:51 And that's how we find 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:

$4^4=$

Step-by-step solution

To solve the problem of determining $4^4$ , we follow a straightforward calculation of powers:

Step 1: Understand the expression $4^4$ which means $4$ multiplied by itself 4 times.

Step 2: Calculate:

First multiplication: $4 \times 4 = 16$ .
Second multiplication: $16 \times 4 = 64$ .
Third multiplication: $64 \times 4 = 256$ .

Thus, $4^4$ results in an integer value of 256.

Therefore, the solution to the problem is $256$ .

Final Answer

256

Key Points to Remember

Essential concepts to master this topic

Rule: $4^4$ means multiply 4 by itself 4 times
Technique: Calculate step by step: $4 \times 4 = 16$ , then $16 \times 4 = 64$ , then $64 \times 4 = 256$
Check: Verify by counting multiplications: 4 appears exactly 4 times in the calculation ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying the base
Don't calculate $4^4$ as 4 + 4 + 4 + 4 = 16! This confuses addition with exponentiation and gives completely wrong answers. Always multiply the base by itself the number of times shown in the exponent.

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

What does the small number 4 on top mean?

The small number is called an exponent. It tells you how many times to multiply the base number by itself. So $4^4$ means multiply 4 by itself 4 times.

Why can't I just multiply 4 × 4 to get 16?

That would only be $4^2$ ! For $4^4$ , you need to keep multiplying: 4 × 4 × 4 × 4. Count carefully - there should be exactly 4 fours being multiplied together.

Is there a faster way than multiplying step by step?

For small exponents like this, step-by-step is actually the safest method. As you get more advanced, you might learn about patterns with powers, but building your multiplication skills first is most important!

How do I know if 256 is the right answer?

You can work backwards! Try to think: what number times 4 equals 256? It's 64. What times 4 equals 64? It's 16. What times 4 equals 16? It's 4. Perfect!

What if I get confused about how many times to multiply?

Write it out the long way first: $4^4 = 4 \times 4 \times 4 \times 4$ . Count the fours - there should be exactly 4 of them. Then multiply from left to right, two at a time.

🌟 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