Find the Missing Exponent in 12^□ = 12×12×12: Index Notation

Q: What's the difference between the base and the exponent?

The base is the number being multiplied (12 in this case), and the exponent tells you how many times to use the base as a factor in multiplication.

Q: Why isn't the answer 4 or 6?

These are common wrong answers! 4 might come from adding instead of counting factors, and 6 might come from counting symbols incorrectly. Always focus on counting the base numbers, not operations.

Q: What if there were more 12's multiplied together?

Just keep counting! $ 12 \times 12 \times 12 \times 12 $ would be $ 12^4 $, and $ 12 \times 12 \times 12 \times 12 \times 12 $ would be $ 12^5 $.

Exponent Rules with Repeated Multiplication

Fill in the missing number:

$12^☐=12\cdot12\cdot12$

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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

00:15 Let's use this formula in our exercise

00:23 X is the number being multiplied

00:27 The number of multiplications equals the exponent (N)

00:33 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:

$12^☐=12\cdot12\cdot12$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Exponent equals the number of times base is multiplied
Technique: Count multiplication symbols: 12×12×12 has 3 factors of 12
Check: Verify that $12^3 = 12 \times 12 \times 12 = 1728$ ✓

Common Mistakes

Avoid these frequent errors

Counting the base number instead of multiplication factors
Don't count 12 as the exponent just because you see it repeated = wrong answer of 12! The exponent represents how many times the base multiplies itself, not the base value. Always count the number of factors in the multiplication.

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

How do I know what the exponent should be?

Count how many times the base number appears in the multiplication. In $12 \times 12 \times 12$ , the number 12 appears 3 times, so the exponent is 3.

What's the difference between the base and the exponent?

The base is the number being multiplied (12 in this case), and the exponent tells you how many times to use the base as a factor in multiplication.

Why isn't the answer 4 or 6?

These are common wrong answers! 4 might come from adding instead of counting factors, and 6 might come from counting symbols incorrectly. Always focus on counting the base numbers, not operations.

How can I check if my exponent is right?

Expand the exponential form back to multiplication and count. $12^3$ means $12 \times 12 \times 12$ - that's exactly 3 factors of 12!

What if there were more 12's multiplied together?

Just keep counting! $12 \times 12 \times 12 \times 12$ would be $12^4$ , and $12 \times 12 \times 12 \times 12 \times 12$ would be $12^5$ .

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