What is the definition of power to a power in math? What is the meaning of power of a power?

The definition of power to a power is simple.

Definition of power to a power:

Power of a power is a power with the same base and its exponent is equal to the product of the exponents.

Power of a power formula

(a^{m})^{n} = a^{m * n} |

Example 1.

Power of a power

(4^{2})^{3} =4 ^{2 * 3} =4 ^{6} = 4096 |

See Powers of 4.

Example 2.

A power with a positive base and a negative exponent of a positive power

(4^{-2})^{3} =4 ^{-2 * 3} =4 ^{-6} = | ||

1 | = | 1 |
---|---|---|

4^{6} | 4096 |

See Powers of 4.

Example 3.

A power with a positive base and a positive exponent of a negative power

(4^{2})^{-3} =4 ^{2 * (-3)} =4 ^{-6} = | ||

1 | = | 1 |
---|---|---|

4^{6} | 4096 |

See Powers of 4.

Example 4.

A power with a positive base and a negative exponent of a negative power

(4^{-2})^{-3} =4 ^{-2 * (-3)} =4 ^{6} = 4096 |

See Powers of 4.