Level: 6 - 9, middle

Asking: Student

Question:

What are the last two digits of:

- 3 to the power of 1994
- 7 to the power of 1994
- 3 to the power of 1994 + 7 to the power of 1994
- 7 to the power of 1994 - 3 to the power of 1994

The key here is to see the pattern.

3 to the power of 1 | = | 3 |

3 to the power of 2 | = | 9 |

3 to the power of 3 | = | 27 |

3 to the power of 4 | = | 81 |

3 to the power of 5 | = | 243 |

3 to the power of 6 | = | 729 |

3 to the power of 7 | = | 2187 |

3 to the power of 8 | = | 6561 |

3 to the power of 9 | = | 19683 |

If you divide 1994 by 4 you find the 1994 = 4 * 498 + 2.

Thus,

3 to the power of 1992 ends in a 1

3 to the power of 1993 ends in a 3

and

3 to the power of 1994 ends in a 9

Cheers,

Penny

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