Compare Powers: Is 6¹ Greater Than 1⁶?

Exponent Rules with Base Comparisons

Which is larger?

$6^1\text{ }_{——}1^6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine which is greater?

00:06 Any number to the power of 1 equals the number itself

00:10 1 to the power of any number always equals 1

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Which is larger?

$6^1\text{ }_{——}1^6$

2

Step-by-step solution

To solve this problem, we'll compare the two expressions $6^1$ and $1^6$ by computing each power:

Step 1: Calculate $6^1$ .
Since the exponent is 1, $6^1 = 6$ .
Step 2: Calculate $1^6$ .
Any number raised to a power of 6 is multiplied by itself six times. Here, $1^6 = 1 \times 1 \times 1 \times 1 \times 1 \times 1 = 1$ .
Step 3: Compare the results.
$6^1 = 6$ and $1^6 = 1$ .

Since $6 > 1$ , we conclude that $6^1$ is larger than $1^6$ .

Therefore, the answer is $>$ .

3

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Fundamental Rule: Any number to the power of 1 equals itself
Technique: Calculate each power separately: $6^1 = 6$ and $1^6 = 1$
Check: Compare final values numerically: 6 > 1, so $6^1 > 1^6$ ✓

Common Mistakes

Avoid these frequent errors

Assuming larger exponents always mean larger results
Don't think $1^6 > 6^1$ because 6 > 1 as exponents = wrong answer 1 > 6! The base matters more than exponent size when bases differ greatly. Always calculate each power completely before comparing.

Practice Quiz

Test your knowledge with interactive questions

$\( 11^2= \)$

FAQ

Everything you need to know about this question

Why is $1^6$ equal to 1?

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The number 1 raised to any power always equals 1! This is because $1^6 = 1 \times 1 \times 1 \times 1 \times 1 \times 1 = 1$ .

What if the exponent was 0 instead of 1?

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Any non-zero number raised to the power of 0 equals 1. So $6^0 = 1$ , making $6^0 = 1^6$ in that case!

Does the order of comparison matter?

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Yes! $6^1 > 1^6$ means 6 is greater than 1. If you wrote $1^6 < 6^1$ , that would also be correct but means 1 is less than 6.

How do I remember which symbol to use?

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Think of the symbol as an arrow pointing to the smaller number. Since 1 < 6, the point of < faces the 1, giving us $1^6 < 6^1$ or $6^1 > 1^6$ .

What if both bases and exponents were different?

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Calculate each power completely first! For example, with $2^3$ vs $3^2$ : find $2^3 = 8$ and $3^2 = 9$ , then compare 8 vs 9.

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