2. Вычислите: 1) a) 3⁷⋅3⁻⁶; 6) 7⁻⁹⋅7⁸; B) (\frac{1}{5})^{-7}⋅(\frac{1}{5})^{6}; r) (\frac{1}{7})^{14}⋅(\frac{1}{4})^{-16}; 2) a) 2⁵:2⁶; б) 5:5⁻²; B) 6⁻⁹:6⁻¹¹; Г) ((\frac{1}{6})^{-3})^{-2}; 3) a) (3²)⁻¹; 6) ((\frac{1}{2})^{-3})^{-2}; в) (0,1⁻²)⁶; г) ((\frac{1}{7})^{-2})⁰; 4) a) -17⋅34⁻¹; 6) -10⋅2⁻³; B) (\frac{1}{8})^{-2}⋅0,01⁻¹; г) 6⁻²+24⁻¹; 5) a) 32⋅2⁻⁶; 6) 27⋅(3⁻²)²; B) 7⁻⁸⋅7⁹:49; г) 25⁻²⋅(\frac{1}{5})^{-6}; 6) a) 81⁻²⋅27²; 6) 16⁻⁵:8⁻⁶; в) (\frac{-6}{15})^{-9.6^{-7}}; г) \frac{4^{-6}⋅16^{-5}}{8^{-10}}.

Question

Вопрос:

2. Вычислите: 1) a) 3⁷⋅3⁻⁶; 6) 7⁻⁹⋅7⁸; B) (\frac{1}{5})^{-7}⋅(\frac{1}{5})^{6}; r) (\frac{1}{7})^{14}⋅(\frac{1}{4})^{-16}; 2) a) 2⁵:2⁶; б) 5:5⁻²; B) 6⁻⁹:6⁻¹¹; Г) ((\frac{1}{6})^{-3})^{-2}; 3) a) (3²)⁻¹; 6) ((\frac{1}{2})^{-3})^{-2}; в) (0,1⁻²)⁶; г) ((\frac{1}{7})^{-2})⁰; 4) a) -17⋅34⁻¹; 6) -10⋅2⁻³; B) (\frac{1}{8})^{-2}⋅0,01⁻¹; г) 6⁻²+24⁻¹; 5) a) 32⋅2⁻⁶; 6) 27⋅(3⁻²)²; B) 7⁻⁸⋅7⁹:49; г) 25⁻²⋅(\frac{1}{5})^{-6}; 6) a) 81⁻²⋅27²; 6) 16⁻⁵:8⁻⁶; в) (\frac{-6}{15})^{-9.6^{-7}}; г) \frac{4^{-6}⋅16^{-5}}{8^{-10}}.

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Accepted Answer

2. Вычислите:

1)

a) 3⁷⋅3⁻⁶ = 3⁽⁷⁻⁶⁾ = 3¹ = 3

б) 7⁻⁹⋅7⁸ = 7⁽⁻⁹⁺⁸⁾ = 7⁻¹ = \frac{1}{7}

в) (\frac{1}{5})^{-7}⋅(\frac{1}{5})^{6} = (\frac{1}{5})^{(-7+6)} = (\frac{1}{5})^{-1} = 5

г) (\frac{1}{7})^{14}⋅(\frac{1}{4})^{-16} = (\frac{1}{7})^{14}⋅(4)^{16}

2)

a) 2⁵:2⁶ = 2^(5-6) = 2^(-1) = \frac{1}{2}

б) 5:5⁻² = 5^(1-(-2)) = 5^(1+2) = 5³ = 125

в) 6⁻⁹:6⁻¹¹ = 6^(-9-(-11)) = 6^(-9+11) = 6² = 36

г) ((\frac{1}{6})^{-3})^{-2} = (\frac{1}{6})^{(-3)⋅(-2)} = (\frac{1}{6})^{6} = \frac{1}{46656}

3)

a) (3²)⁻¹ = 3^(2*(-1)) = 3^(-2) = \frac{1}{3^2} = \frac{1}{9}

б) ((\frac{1}{2})^{-3})^{-2} = (\frac{1}{2})^((-3)*(-2)) = (\frac{1}{2})^6 = (\frac{1}{64})

в) (0,1⁻²)⁶ = (\frac{1}{10})^{-12} = (10)^{12}

г) ((\frac{1}{7})^{-2})⁰ = (\frac{1}{7})^((-2)*0) = (\frac{1}{7})^0 = 1

4)

a) -17⋅34⁻¹ = -17⋅\frac{1}{34} = -\frac{17}{34} = -\frac{1}{2}

б) -10⋅2⁻³ = -10⋅\frac{1}{2^3} = -10⋅\frac{1}{8} = -\frac{10}{8} = -\frac{5}{4}

в) (\frac{1}{8})^{-2}⋅0,01⁻¹ = 8²⋅(0,01)⁻¹ = 64⋅(100) = 6400

г) 6⁻²+24⁻¹ = (\frac{1}{6})² + \frac{1}{24} = \frac{1}{36} + \frac{1}{24} = \frac{2}{72} + \frac{3}{72} = \frac{5}{72}

5)

a) 32⋅2⁻⁶ = 32⋅\frac{1}{2^6} = 32⋅\frac{1}{64} = \frac{32}{64} = \frac{1}{2}

б) 27⋅(3⁻²)² = 27⋅3^(-4) = 3^3 ⋅ 3^(-4) = 3^(-1) = \frac{1}{3}

в) 7⁻⁸⋅7⁹:49 = 7⁻⁸⋅7⁹ : 7² = 7^(-8+9-2) = 7^(-1) = \frac{1}{7}

г) 25⁻²⋅(\frac{1}{5})^{-6} = (5²)⁻²⋅5⁶ = 5^(-4)⋅5⁶ = 5² = 25

6)

a) 81⁻²⋅27² = (3⁴)⁻² ⋅ (3³) ² = 3⁻⁸ ⋅ 3⁶ = 3⁻² = \frac{1}{9}

б) 16⁻⁵:8⁻⁶ = (2⁴)⁻⁵ : (2³)⁻⁶ = 2⁻²⁰ : 2⁻¹⁸ = 2⁻²⁰⁻⁽⁻¹⁸⁾ = 2⁻²⁰⁺¹⁸ = 2⁻² = (\frac{1}{4})

в) (\frac{-6}{15})^{-9.6^{-7}} = (\frac{-6}{15})^{-9} ⋅ (\frac{-6}{15})^{-6} ⋅ (\frac{-6}{15})^{-7}

г) \frac{4^{-6}⋅16^{-5}}{8^{-10}} = \frac{(2^2)^{-6}⋅(2^4)^{-5}}{(2^3)^{-10}} = \frac{2^{-12}⋅2^{-20}}{2^{-30}} = \frac{2^{-32}}{2^{-30}} = 2^{-32+30} = 2^{-2} = \frac{1}{4}