2. Вычислите: 1) a) 3⁹ · 3⁻⁸; б) 5⁻¹⁰ · 5⁹; в) (1/7)⁻⁴ · (1/7)³; г) (1/3)⁷ · (1/3)⁻⁹; 2) a) 6⁶ : 6⁷; б) 6 : 6⁻²; в) 5⁻⁴ : 5⁻⁶; г) (1/5)⁻³ : (1/5)⁻³; 3) a) (8²)⁻¹; б) ((1/3)⁻¹)⁰; в) (0,4⁻¹)³; г) ((1/5)⁻²)⁻²; 4) a) -17 · 51⁻¹; б) -14 · 7⁻²; в) (1/4)⁻³ - 0,01⁻¹; г) 7⁻² + 21⁻¹; 5) a) 81 · 3⁻⁵; б) 27 · (3⁻²)²; в) 7⁻⁶ · 7⁷ : 49; г) 64⁻³ · (1/6)⁻⁷

1)

a) 3⁹ ⋅ 3⁻⁸ = 3^(9+(-8)) = 3¹ = 3

б) 5⁻¹⁰ ⋅ 5⁹ = 5^(-10+9) = 5⁻¹ = 1/5

в) (1/7)⁻⁴ ⋅ (1/7)³ = (1/7)^(-4+3) = (1/7)⁻¹ = 7

г) (1/3)⁷ ⋅ (1/3)⁻⁹ = (1/3)^(7-9) = (1/3)⁻² = 3² = 9

2)

a) 6⁶ : 6⁷ = 6^(6-7) = 6⁻¹ = 1/6

б) 6 : 6⁻² = 6^(1-(-2)) = 6³ = 216

в) 5⁻⁴ : 5⁻⁶ = 5^(-4-(-6)) = 5² = 25

г) (1/5)⁻³ : (1/5)⁻³ = (1/5)^(-3-(-3)) = (1/5)⁰ = 1

3)

a) (8²)⁻¹ = 8^(2*(-1)) = 8⁻² = 1/8² = 1/64

б) ((1/3)⁻¹)⁰ = (1/3)^(-1*0) = (1/3)⁰ = 1

в) (0,4⁻¹)³ = (4/10)⁻³ = (10/4)³ = (5/2)³ = 125/8 = 15,625

г) ((1/5)⁻²)⁻² = (1/5)^(-2*(-2)) = (1/5)⁴ = 1/625 = 0,0016

4)

a) -17 ⋅ 51⁻¹ = -17 ⋅ (1/51) = -17/51 = -1/3

б) -14 ⋅ 7⁻² = -14 ⋅ (1/7²) = -14/49 = -2/7

в) (1/4)⁻³ - 0,01⁻¹ = 4³ - (1/100)⁻¹ = 64 - 100 = -36

г) 7⁻² + 21⁻¹ = 1/7² + 1/21 = 1/49 + 1/21 = 3/147 + 7/147 = 10/147

5)

a) 81 ⋅ 3⁻⁵ = 3⁴ ⋅ 3⁻⁵ = 3^(4-5) = 3⁻¹ = 1/3

б) 27 ⋅ (3⁻²)² = 3³ ⋅ 3^(-2*2) = 3³ ⋅ 3⁻⁴ = 3^(-4+3) = 3⁻¹ = 1/3

в) 7⁻⁶ ⋅ 7⁷ : 49 = 7^(-6+7) : 7² = 7¹ : 7² = 7^(1-2) = 7⁻¹ = 1/7

г) 64⁻³ ⋅ (1/6)⁻⁷ = (2⁶)⁻³ ⋅ 6⁷ = 2^(-3*6) ⋅ 6⁷ = 2⁻¹⁸ ⋅ 6⁷ = (1/2¹⁸) ⋅ 6⁷ = (2*3)⁷/2¹⁸ = 2⁷*3⁷/2¹⁸ = 3⁷/2¹¹ = 2187/2048