Compare Powers: Which is Greater, 5² or 2⁵?

Q: Why isn't the bigger base always bigger?

The exponent matters more than base size! A smaller base raised to a higher power can be larger. For example, $ 2^{10} = 1024 $ is much bigger than $ 10^2 = 100 $.

Q: How can I remember powers of 2?

Powers of 2 follow a doubling pattern: $ 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32 $. Each one doubles the previous!

Q: Can I use a calculator for these problems?

Check with your teacher first. For basic powers like $ 5^2 $ and $ 2^5 $, you should be able to calculate by hand. Practice builds number sense!

Exponent Comparison with Different Bases

Which is larger?

$5^2\text{ }_{——}2^5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine which is bigger?

00:03 Break down each exponent into multiplications

00:13 Calculate the multiplications

00:32 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

Which is larger?

$5^2\text{ }_{——}2^5$

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Calculate $5^2$ .
Step 2: Calculate $2^5$ .
Step 3: Compare the results to determine which is larger.

Let's work through each step:
Step 1: Calculate $5^2$ .
$5^2 = 5 \times 5 = 25$ .

Step 2: Calculate $2^5$ .
$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$ .

Step 3: Compare the results.
We have $5^2 = 25$ and $2^5 = 32$ . Clearly, $25 < 32$ .

Therefore, $5^2 \text{ }_{——} 2^5$ is $<$ .

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Calculate each power completely before comparing values
Technique: $5^2 = 5 \times 5 = 25$ and $2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$
Check: Verify calculations by substituting: 25 < 32, so $5^2 < 2^5$ ✓

Common Mistakes

Avoid these frequent errors

Comparing exponents instead of values
Don't think 'bigger base means bigger result' = $5^2 > 2^5$ wrong! Base size doesn't determine final value when exponents differ. Always calculate the actual numerical values first.

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 isn't the bigger base always bigger?

The exponent matters more than base size! A smaller base raised to a higher power can be larger. For example, $2^{10} = 1024$ is much bigger than $10^2 = 100$ .

Do I need to multiply out every single factor?

Yes! Write out each multiplication step to avoid errors. For $2^5$ , show: 2 × 2 = 4, then 4 × 2 = 8, then 8 × 2 = 16, then 16 × 2 = 32.

How can I remember powers of 2?

Powers of 2 follow a doubling pattern: $2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32$ . Each one doubles the previous!

What if the bases and exponents are both different?

Same method! Calculate each power completely, then compare the final numbers. Never try to guess based on just looking at bases and exponents.

Can I use a calculator for these problems?

Check with your teacher first. For basic powers like $5^2$ and $2^5$ , you should be able to calculate by hand. Practice builds number sense!

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