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# Index Numbers

### Consolidation

Question | Answer |
---|---|

The Base number | is the number that will be multiplied |

The Index number | tells us how many times it will multiply itself |

Another name for 'Index' | Power |

The opposite of subtraction is | Addition |

The opposite of addition is | Subtraction |

The opposite of multiplication is | Division |

The opposite of division is | Multiplication |

When we multiply powers we | add them |

When we divide powers we | subtract them |

When there are powers outside a bracket we ( m^2) ^6 | multiply the powers inside the bracket = m^12 |

What is 12^3? | 12 x 12 x 12 |

What is 8 x 8 x 8 x 8? | 8^4 |

In algebraic fractions do we simplify the numbers or the pronumerals first? eg 6x/3f | numbers- eg 3 goes into both 6 and 3 so my answer is 2x/f |

Simplify 20km/15lx- | 5 goes into both 20 and 15 so my answer is 4km/3lx, |

Simplify 15mn/18mk- | 3 goes into both 15 and 18 making 5mn/6mk, then there's an m on the top & on the bottom so I subtract them= 5n/6k |

Anything to the power of zero is | 1 |

m^0 = | 1 |

23g^0 = | 23 ( 23 x 1) |

4g= | 4 times g |

12ghm= | 12 x g x h x m |

24/6 = | 24 divided by 6 |

Y/9 = | Y divided by 9 |

6(m + 2) = | 6m + 12 |

m ( 2 + 6) = | 8m |

f ( 2 +3) everything inside the brackets | gets done first ... 2+3 =5, times f so my answer is 5f |

3 ( f + 2) everything inside the brackets | gets multiplied by the number outside the bracket ... 3f + 6 |

( d^3) ^5 = | d ^15 |

(z^2)^4 = | z ^8 |

brackets means | times or multiply |

( k^3/m^6) ^2 = | k^6/m^12 |

( j^2/w ^5 ) ^4 = | j^8/ w^20 |

(2m^3) ^ 2 = | 2^2 times m^6 = 4m^6 ( 2 squared equals 4) |

(2y^4) ^ 3 = | 2^3 times y^12 = 8y^12 ( 2x2x2 = 8) |

5 ( 2g + hm) = | 10g + 5hm |