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

Which of the following is equivalent to the expression below?

$\( \)$ $\( 10,000^1 \)$

FAQ

Everything you need to know about this question

Why is $1^6$ equal to 1?

+

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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