Find the Missing Exponent in 4^☐ = 4×4×4×4: Power Equation Solver

Q: Why isn't the exponent 256 if that's what 4×4×4×4 equals?

The exponent tells you how many times to multiply, not what the final answer is! $ 4^4 $ means "multiply 4 by itself 4 times" and the result happens to be 256.

Q: How do I count the factors correctly?

Count each appearance of the base number. In $ 4 \cdot 4 \cdot 4 \cdot 4 $, the number 4 appears 4 times, so the exponent is 4.

Q: What if the base appears different numbers of times?

The exponent always matches the count! If you see $ 3 \cdot 3 \cdot 3 $, that's $ 3^3 $ because 3 appears 3 times.

Q: Is there a difference between 4⁴ and 4×4×4×4?

No difference at all! $ 4^4 $ is just the shorter way to write $ 4 \times 4 \times 4 \times 4 $. They mean exactly the same thing.

Q: What if I see 4¹ or 4²?

$ 4^1 = 4 $ (just one 4) and $ 4^2 = 4 \times 4 = 16 $ (two 4's multiplied). The pattern continues: the exponent = number of factors!

Exponent Rules with Repeated Multiplication

Fill in the missing number:

$4^☐=4\cdot4\cdot4\cdot4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing number

00:03 Let's use the power formula

00:06 Any number (X) raised to any power (N)

00:09 equals X multiplied by itself N times

00:17 Let's use this formula in our exercise

00:27 X is the number being multiplied

00:32 The number of multiplications equals the exponent (N)

00:37 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

Fill in the missing number:

$4^☐=4\cdot4\cdot4\cdot4$

Step-by-step solution

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

Step 1: Identify how many times 4 is multiplied by itself in the expression $4 \cdot 4 \cdot 4 \cdot 4$ .
Step 2: Determine the exponent that matches this count.

Now, let's work through each step:
Step 1: In the expression $4 \cdot 4 \cdot 4 \cdot 4$ , the base number 4 is multiplied by itself 4 times.
Step 2: According to the rule of exponents, $a^n$ is the notation for a number $a$ multiplied by itself $n$ times.

Therefore, the correct exponent for $4$ in the expression is 4, so the missing number is $\mathbf{4}$ . The complete expression is $4^4$ .

Therefore, the solution to the problem is $4$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: The exponent equals the number of times the base is multiplied
Technique: Count factors: $4 \cdot 4 \cdot 4 \cdot 4$ has 4 factors of 4
Check: Verify $4^4 = 4 \times 4 \times 4 \times 4 = 256$ ✓

Common Mistakes

Avoid these frequent errors

Counting the total value instead of multiplication instances
Don't calculate $4 \times 4 \times 4 \times 4 = 256$ and use 256 as the exponent! The exponent isn't the answer to the multiplication. Always count how many times the base appears as a factor.

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

Why isn't the exponent 256 if that's what 4×4×4×4 equals?

The exponent tells you how many times to multiply, not what the final answer is! $4^4$ means "multiply 4 by itself 4 times" and the result happens to be 256.

How do I count the factors correctly?

Count each appearance of the base number. In $4 \cdot 4 \cdot 4 \cdot 4$ , the number 4 appears 4 times, so the exponent is 4.

What if the base appears different numbers of times?

The exponent always matches the count! If you see $3 \cdot 3 \cdot 3$ , that's $3^3$ because 3 appears 3 times.

Is there a difference between 4⁴ and 4×4×4×4?

No difference at all! $4^4$ is just the shorter way to write $4 \times 4 \times 4 \times 4$ . They mean exactly the same thing.

What if I see 4¹ or 4²?

$4^1 = 4$ (just one 4) and $4^2 = 4 \times 4 = 16$ (two 4's multiplied). The pattern continues: the exponent = number of factors!

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