There are many interesting patterns to be found in the tables of powers of whole numbers.
Powers of 2 
Powers of 3 
Powers of 4 
2^{1} = 2  3^{1} = 3  4^{1} = 4 
2^{2} = 4  3^{2} = 9  4^{2} = 16 
2^{3} = 8  3^{3} = 27  4^{3} = 64 
2^{4} = 16  3^{4} = 81  4^{4} = 256 
2^{5} = 32  3^{5} = 243  4^{5} = 1024 
2^{6} = 64  3^{6} = 729  4^{6} = 4096 
2^{7} = 128  3^{7} = 2187  4^{7} = 16384 
2^{8} = 256  3^{8} = 6561  4^{8} = 65536 
2^{9} = 512  3^{9} = 19683  4^{9} = 262144 
2^{10} = 1024  3^{10} = 59049  4^{10} = 1048576 
One thing you may notice are the patterns in the one's digits. In the powers of 2 table, the ones digits form the repeating pattern 2, 4, 8, 6, 2, 4, 8, 6.... In the powers of 3 table, the ones digits form the repeating pattern 3, 9, 7, 1, 3, 9, 7, 1.... We leave it to you to figure out why this happens!
In the powers of 4 table, the ones digits alternate: 4, 6, 4, 6. In fact, you can see that the powers of 4 are the same as the even powers of 2:
4^{1} = 2^{2}
4^{2} = 2^{4}
4^{3} = 2^{6}
etc.
The same relationship exists between the powers of 3 and the powers of 9:
Powers of 3 
Powers of 9 
3^{1} = 3  9^{1} = 9 
3^{2} = 9  9^{2} = 81 
3^{3} = 27  9^{3} = 729 
3^{4} = 81  9^{4} = 6561 
3^{5} = 243  9^{5} = 59,049 
3^{6} = 729  9^{6} = 531,441 
3^{7} = 2187  9^{7} = 4,782,969 
3^{8} = 6561  9^{8} = 43,046,721 
3^{9} = 19,683  9^{9} = 387,420,489 
3^{10} = 59,049  9^{10} = 3,486,784,401 
The powers of 10 are easy, because we use base 10: for 10^{n} just write a "1" with n zeros after it. For negative powers 10^{n}, write "0." followed by n – 1 zeros, and then a 1. The powers of 10 are widely used in scientific notation, so it's a good idea to get comfortable with them.
Powers of 10 

10^{1} = 10  10^{0} = 1 
10^{2} = 100  10^{1} = 0.1 
10^{3} = 1000  10^{2} = 0.01 
10^{4} = 10,000  10^{3} = 0.001 
10^{5} = 100,000 (one hundred thousand) 
10^{4} = 0.0001 (one ten thousandth) 
10^{6} = 1,000,000 (one million) 
10^{5} = 0.00001 (one hundred thousandth) 
10^{7} = 10,000,000 (ten million) 
10^{6} = 0.000001 (one millionth) 
10^{8} = 100,000,000 (one hundred million) 
10^{7} = 0.0000001 (one ten millionth) 
10^{9} = 1,000,000,000 (one billion) 
10^{8} = 0.00000001 (one hundred millionth) 
10^{10} = 10,000,000,000 (ten billion) 
10^{9} = 0.000000001 (one billionth) 
Click here for more names for really big and really small numbers.
Another consequence of our use of base 10 is a nice pattern between the negative powers of 2 and the powers of 5.
Powers of 2 
Powers of 5 
2^{5} = 1/32 = 0.03125  5^{5} = 1/3125 = 0.00032 
2^{4} = 1/16 = 0.0625  5^{4} = 1/625 = 0.0016 
2^{3} = 1/8 = 0.125  5^{3} = 1/125 = 0.008 
2^{2} = 1/4 = 0.25  5^{2} = 1/25 = 0.04 
2^{1} = 1/2 = 0.5  5^{1} = 1/5 = 0.2 
2^{0} = 1  5^{0} = 1 