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

Question

Which is larger?

$2^4\text{ }_{——}4^2$

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!

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 $=$ .

$=$