Compare Powers: Is 2^4 Greater Than 4^2?

Q: How do I remember what the exponent means?

The exponent tells you how many times to use the base as a factor. So $ 2^4 $ = 2 × 2 × 2 × 2, and $ 4^2 $ = 4 × 4. Count the base number that many times!

Q: Could other powers also be equal like this?

Yes! For example, $ 8^2 = 64 $ and $ 4^3 = 64 $ are also equal. When different bases and exponents give the same result, we call these equivalent powers.

Comparing Powers with Equal Bases

Which is larger?

$2^4\text{ }_{——}4^2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's figure out which one is bigger.

00:12 First, break down the exponent into multiplications.

00:17 Now, calculate these multiplications.

00:22 Then, change the multiplication back to an exponent.

00:27 You'll see that both values are equal.

00:30 And that's how we solve the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which is larger?

$2^4\text{ }_{——}4^2$

Step-by-step solution

To solve this problem, we will calculate $2^4$ and $4^2$ and then compare the results:

Step 1: Calculate $2^4$
$2^4$ means multiplying 2 by itself 4 times: $2 \times 2 \times 2 \times 2 = 16$ .
Step 2: Calculate $4^2$
$4^2$ means multiplying 4 by itself 2 times: $4 \times 4 = 16$ .
Step 3: Compare the results
Since both calculations result in 16, we have $2^4 = 4^2$ .

Therefore, the correct comparison is that $2^4$ is equal to $4^2$ . The answer to the problem is $=$ .

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Exponent Rule: Calculate each power separately before comparing values
Technique: $2^4 = 2 \times 2 \times 2 \times 2 = 16$
Check: Both $2^4$ and $4^2$ equal 16, so they're equal ✓

Common Mistakes

Avoid these frequent errors

Comparing exponents instead of calculating the actual values
Don't just look at 4 vs 2 and think $2^4 > 4^2$ because 4 > 2! This ignores how exponents actually work and gives wrong comparisons. Always calculate the full value of each power first, then compare the results.

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

Why can't I just compare the exponents 4 and 2?

Because exponents work differently than regular numbers! The base numbers (2 and 4) are different, so you must calculate the actual values. $2^4$ means four 2's multiplied together, while $4^2$ means two 4's multiplied together.

How do I remember what the exponent means?

The exponent tells you how many times to use the base as a factor. So $2^4$ = 2 × 2 × 2 × 2, and $4^2$ = 4 × 4. Count the base number that many times!

Could other powers also be equal like this?

Yes! For example, $8^2 = 64$ and $4^3 = 64$ are also equal. When different bases and exponents give the same result, we call these equivalent powers.

What if the numbers were much bigger?

Use the same method! Calculate each power step by step, or use patterns. For very large numbers, you might need a calculator, but the process stays the same: compute each side, then compare.

Is there a shortcut for comparing powers?

Sometimes! If you notice that one base is a power of the other (like 4 = $2^2$ ), you can rewrite: $4^2 = (2^2)^2 = 2^4$ . But when starting out, always calculate both sides fully.

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