### Multiplying Powers

When you multiply two powers with the SAME base number, you add the indices:

- Example 1. work out 2
^{2}× 2^{3} the base is 2 - Example 2. work out 3
^{2}× 3^{4} the base is 3 - Example 3. work out 2
^{2}× 2^{3}× 3^{3}

2^{2} = 2 × 2 = 4 |

2^{3} = 2 × 2 × 2 = 8 |

2^{2} × 2^{3} | = | 2 × 2 × 2 × 2 × 2 |

= | 2^{2+3} = 2^{5} = 32 |

3^{2} = 3 × 3 = 9 |

3^{4} = 3 × 3 × 3 × 3 = 81 |

3^{2} × 3^{4} | = | 3 × 3 × 3 × 3 × 3 × 3 |

= | 3^{2+4} = 3^{6} = 729 |

there are two bases:

two are base 2; and one is base 3

2^{2} × 2^{3} × 3^{3} |

= | 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 | |

= | 2^{2+3} × 3^{3} = 2^{5} × 3^{3} | |

= | 32 × 27 = 864 |