Powers of Ten

Powers of 10 are the easiest powers there are. ${10}^{2}$ is $10\cdot 10$, which is 100. ${10}^{3}$ is $10\cdot 10\cdot 10$, which is 1000. Each extra factor of 10 adds one more zero.

That is because multiplying by 10 puts a zero on the end of a number. So 10 to a power is a 1 followed by that many zeros: ${10}^{5}$ is 100000, and ${10}^{6}$ is 1000000, a million. No multiplying needed, just counting.

A number times a power of 10 works the same way. $3\cdot {10}^{5}$ is $3\cdot 100000$, and multiplying 3 by 100000 puts five zeros after the 3: 300000. Scientists write huge numbers like this, because the exponent tells you the size at a glance.