How to write an expression as a power?

See the following examples.

Problem 1: Write the expression as a single power then evaluate

2^{2} * 2^{5}

Solution:

2^{2} * 2^{5} =2 ^{2 + 5} =2 ^{7} = 128 |

Siehe Powers of 2.

Problem 2: Write the expression as a single power then evaluate

15^{3} * 4^{3}

Solution:

15^{3} * 4^{3} =(15 * 4) ^{3} =60 ^{3} = 216000 |

Problem 3: Write the expression as a single power then evaluate

3^{2} * 3^{5} * 3

Solution:

3^{2} * 3^{5} * 3 =3 ^{2} * 3^{5} * 3^{1} =3 ^{2 + 5 + 1} =3 ^{8} = 6561 |

Siehe Powers of 3.

Problem 4: Write the expression as a single power then evaluate

6^{2} * 6^{3} * 4^{5}

Solution:

6^{2} * 6^{3} * 4^{5} =6 ^{2 + 3} * 4^{5} =6 ^{5} * 4^{5} =(6 * 4) ^{5} =24 ^{5} = 7962624 |

Problem 5: Write as a single power then evaluate

32^{2} : 2^{2}

Solution:

32^{2} : 2^{2} =(32 : 2) ^{2} =16 ^{2} = 256 |

Problem 6: Write as a single power then evaluate

14^{5} : 14^{2}

Solution:

14^{5} : 14^{2} =14 ^{5 - 2} =14 ^{3} = 2744 |

Problem 7: Write as a single power then evaluate

7^{6} * 7^{-2}

Solution:

7^{6} * 7^{-2} =7 ^{6 + (-2)} =7 ^{4} = 2401 |

Siehe Powers of 7.

Problem 8: Write as a single power then evaluate

(-9)^{6} * 9^{2}

Solution:

(-9)^{6} * 9^{2} =(-1) ^{6} * 9^{6} * 9^{2} =1 * 9 ^{6} * 9^{2} =1 * 9 ^{6 + 2} =9 ^{8} = 43046721 |

Siehe Powers of 9.