### About Exponent Rules:

In order to be successful with polynomials, we must have a great understanding of exponents. We begin by looking at the product rule for exponents. We will then look at the various power rules for exponents. These properties will allow us to work more quickly with exponents.

Test Objectives

- Demonstrate a general understanding of exponents
- Demonstrate the ability to use the product rule for exponents
- Demonstrate the ability to use the power rules for exponents

#1:

Instructions: Simplify each.

a) 6^{4} • 6^{3} • 6^{2}

b) n^{4} • n^{7} • n^{9}

c) x^{4} • y^{4} • z^{4}

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#2:

Instructions: Simplify each.

a) 8(xy)^{5}

b) (xy)^{2} • x^{4}

c) $$\left(\frac{5x}{3}\right)^2$$

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#3:

Instructions: Simplify each.

a)$$\left(\frac{x^4y^7}{z^2}\right)^3$$

b) (-2^{4})^{5}

c) (x^{4}y^{3} • -2x^{4}y^{3})^{2}

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#4:

Instructions: Simplify each.

a) -2yx^{2} • (-2x^{2}y^{4})^{2}

b) (-b^{4} • b^{2})^{2}

c) $$\left(\frac{ax^2}{by^4}\right)^3$$

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#5:

Instructions: Simplify each.

a) (j • -h^{3}j^{4})^{3}

b) $$\left(\frac{x^5y^9}{3}\right)^2$$

c) -2q • (-2rq^{3})^{5}

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Written Solutions:

#1:

Solutions:

a) 6^{9}

b) n^{20}

c) (xyz)^{4}

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#2:

Solutions:

a) 8x^{5}y^{5}

b) x^{6}y^{2}

c)

25x^{2} |

9 |

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#3:

Solutions:

a)

x^{12}y^{21} |

z^{6} |

b) -2^{20}

c) 4x^{16}y^{12}

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#4:

Solutions:

a) -8y^{9}x^{6}

b) b^{12}

c)

a^{3}x^{6} |

b^{3}y^{12} |

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#5:

Solutions:

a) -j^{15}h^{9}

b)

x^{10}y^{18} |

9 |

c) 2^{6}q^{16}r^{5}