00:0-1 | In this example were asked to write a to the | |

00:03 | negative third squared in simplest form , without negative or | |

00:09 | zero exponents . Remember that The power rule tells us | |

00:14 | that when we have a power taken to another power | |

00:17 | , Such as a to the negative 3rd squared , | |

00:21 | we multiply the exponents so we have A to the | |

00:26 | -3 times two Or a to the -6 . Finally | |

00:33 | remember from the previous example that A to the negative | |

00:37 | sixth can be written as one over A . To | |

00:41 | the positive sixth , So a to the negative third | |

00:45 | squared simplifies to one over a to the 6th . |

#### DESCRIPTION:

In this example, weâre given the functions f(x) = 3x â 2 (read as âf of x equalsâ¦â) and g(x) = root x, and weâre asked to find the composite functions f(g(9)) (read as âf of g of 9â) and g(f(9). To find f(g(9)), we first find g(9). Since g(x) = root x, we can find g(9) by substituting a 9 in for the x in the function, to get g(9) = root 9, and the square root of 9 is 3, so g(9) = 3. Now, since g(9) = 3, f(g(9)) is the same thing as f(3), so our next step is to find f(3). And remember that f(x) = 3x â 2, so to find f(3), we substitute a 3 in for the x in the function, and we have f(3) = 3 times 3 minus 2. Notice that I always use parentheses when substituting a value into a function, in this case 3. Finally, 3 times 3 minus 2 simplifies to 9 minus 2, or 7, so f(3) = 7. Therefore, f(g(9)) = 7. Next, to find g(f(9), we first find f(9). Since f(x) = 3x - 2, we find f(9) by substituting a 9 in for the x in the function, to get f(9) = 3 times 9 minus 2, which simplifies to 27 â 2, or 25, so f(9) = 25. Now, since f(9) = 25, g(f(9)) is the same thing as g(25), so our next step is to find g(25). And remember that g(x) = root x, so to find g(25), we substitute a 25 in for the x in the function, to get g(25) = root 25. Finally, the square root of 25 is 5, so g(25) = 5. Therefore, g(f(9)) = 5. Itâs important to recognize that

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