3. Используя свойства степеней, найдите значение выражения: 1) a) 37.(32)3:310; 6) 520:(52)5:58; 94 2) a) 37; 6) 85; 6; 46, 3) a) 1012 26.56; б) 516.316 1514; 272.94 в) 812; 126 в) 35.45

3. Используя свойства степеней, найдите значение выражения:

1) a) 3⁷ \(\cdot\) (3²)³:3¹⁰ = 3⁷ \(\cdot\) 3^2\(\cdot\)3:3¹⁰ = 3⁷ \(\cdot\) 3⁶:3¹⁰ = 3⁷⁺⁶:3¹⁰ = 3¹³:3¹⁰ = 3^13-10 = 3³ = 27

Ответ: 27

б) 5²⁰:(5²)⁵:5⁸ = 5²⁰:5^2\(\cdot\)5:5⁸ = 5²⁰:5¹⁰:5⁸ = 5^20-10:5⁸ = 5¹⁰:5⁸ = 5^10-8 = 5² = 25

Ответ: 25

2) a) \(\frac{9⁴}{3⁷}\) = \(\frac{(3²)⁴}{3⁷}\) = \(\frac{3^2\cdot4}{3⁷}\) = \(\frac{3⁸}{3⁷}\) = 3^8-7 = 3¹ = 3

Ответ: 3

б) \(\frac{8⁵}{4⁶}\) = \(\frac{(2³)⁵}{(2²)⁶}\) = \(\frac{2^3\cdot5}{2^2\cdot6}\) = \(\frac{2¹⁵}{2¹²}\) = 2^15-12 = 2³ = 8

Ответ: 8

в) \(\frac{27² \cdot 9⁴}{81²}\) = \(\frac{(3³)² \cdot (3²)⁴}{(3⁴)²}\) = \(\frac{3^3\cdot2 \cdot 3^2\cdot4}{3^4\cdot2}\) = \(\frac{3⁶ \cdot 3⁸}{3⁸}\) = \(\frac{3⁶⁺⁸}{3⁸}\) = \(\frac{3¹⁴}{3⁸}\) = 3^14-8 = 3⁶ = 729

Ответ: 729

3) a) \(\frac{10¹²}{2⁶ \cdot 5⁶}\) = \(\frac\){\(2 \cdot 5\)¹²}{2⁶ \(\cdot\) 5⁶} = \(\frac{2¹² \cdot 5¹²}{2⁶ \cdot 5⁶}\) = 2^12-6 \(\cdot\) 5^12-6 = 2⁶ \(\cdot\) 5⁶ = \(2 \cdot 5\)⁶ = 10⁶ = 1000000

Ответ: 1000000

б) \(\frac{5¹⁶ \cdot 3¹⁶}{15¹⁴}\) = \(\frac\){\(5 \cdot 3\)¹⁶}{15¹⁴} = \(\frac{15¹⁶}{15¹⁴}\) = 15^16-14 = 15² = 225

Ответ: 225

в) \(\frac{12⁶}{3⁵ \cdot 4⁵}\) = \(\frac\){\(3 \cdot 4\)⁶}{3⁵ \(\cdot\) 4⁵} = \(\frac{3⁶ \cdot 4⁶}{3⁵ \cdot 4⁵}\) = 3^6-5 \(\cdot\) 4^6-5 = 3¹ \(\cdot\) 4¹ = 3 \(\cdot\) 4 = 12

Ответ: 12