## 2. Powers and bases

In the previous section, we expressed numbers as powers of 10. This is termed the base of the expression. However the base can be any number so that:

100 | = | 10 × 10 | 10^{2} |
Base 10: Power 2 |

16 | = | 2 × 2 × 2 × 2 | 2^{4} |
Base 2: Power 4 |

27 | = | 3 × 3 × 3 | 3^{3} |
Base 3: Power 3 |

625 | = | 5 × 5 × 5 × 5 | 5^{4} |
Base 5: Power 4 |

and so on …

In power notation (also called scientific notation) any number can be represented as a power of 10 so that:

325 is between 100 (10^{2}) and 1 000 (10^{3}) and is equal to 3.25 × 100 = 3.25 × 10^{2}, 625 400 is between 10^{5} and 10^{6} and is equal to 6.254 × 10^{5}

There are two special cases of powers. Any number raised to the power of 1 is itself, and any number raised to the power 0 equals 1.