WHAT’S 2 TO THE POWER OF 30
Do you ever find yourself standing in the grocery store, scratching your head and thinking, “how many times can I multiply 2 by itself to get 30?” Well, I do. And it’s a lot!
2 x 2
2 x 2 = 4
2 to the power of 0 is 1, so we know that 2^0 = 1.
Then we can apply the same logic for 1 through 3:
2^1 = 2; 2^2 = 4; and finally, 2^3 = 8.
This means that 4 is equal to 2 x 2.
Let’s break down the equation:
2^2 = 4
8 is the square of 2.
8 is the cube of 2.
8 is the fourth power of 2.
16 is a power of two. It’s also a perfect square.
Let’s break it down: 2 x 2 x 2 = 16, so we have our first factor of 4 (2^4). The other factor is 2^2, which gives us 8 as well. Then we multiply those together and add them to get our final answer: 16!
32 is a power of 2, a perfect square and cube, a prime number and a square number.
32=9*4 (or 3*8)
64 is the next power of 2 after 32. This can be seen by looking at the table below:
The reason why 64 is a power of 2 is because it equals 2^4, or 2 times itself 4 times. This means that 64 has been multiplied by itself four times (or expressed as a number in base-2). You might recognize this as being equivalent to 25 which is also a perfect square!
- 128 is the largest number you can represent with a single byte in a computer.
- 128 is the number of possible unique IP addresses.
- 128 is the number of possible unique passwords (excluding letters).
- 128 is also the number of possible unique colors for each pixel on your screen, if you’re using 8-bit color (256 different shades), or 16-bit color (65536 different shades).
The takeaway is that you can use the power of exponents to help you multiply large numbers. For example, if you want to multiply 2 x 3 x 4, instead of writing out all those zeros as we did above and then multiplying them by hand (which would take forever), we can use exponents: 2^3 * 4^2= 2*4*4=16. This saves us time and effort!
Now that you know how exponents work, try some more examples on your own:
This is a fun exercise to help you get a feel for how quickly numbers can grow. I hope that you enjoyed learning about the powers of 2, and maybe even learned something new about yourself along the way!