Вычислите: 1)64^1/2 2)121^1/2 3) (243x 32)^1/5 4)9^8x25^7:225^6 5)-150x128^1/7+35 6)...

Question

Вычислите:

1)64^1/2 2)121^1/2 3) (243x 32)^1/5 4)9^8x25^7:225^6 5)-150x128^1/7+35

6) (1/25)^-6x3125^3/5x(5^-3)+25^5/2x(1/5)^3 7)(25^4)^1/8

Answer 1

1) 64¹/² = (8²)¹/² = 8¹ = 8

2) 121¹/² = (11²)¹/² = 11¹ = 11

3) (243 · 32)¹/⁵  = (3⁵ * 2⁵)¹/⁵ = (3⁵)¹/⁵ * (2⁵)¹/⁵ = 3 * 2 = 6

4) 9⁸ · 25⁷ : 225⁶ =  9*9⁷ · 25⁷ : 225⁶ = 9 · (9·25)⁷ : (225)⁶ =
= 9·(225)⁷ : (225)⁶ = 9 · 225⁷⁻⁶ = 9 · 225 = 2025

5) -150 · 128¹/⁷ + 35 = -150 · (2⁷) ¹/⁷ + 35 = - 150 * 2 + 35 =
= - 300 + 35 = - 265


6) (1/25)⁻⁶ · 3125³/⁵ · 5⁻³ + 25⁵/² · (1/5)³ =
=  25⁶ · (5⁵)³/⁵  · (1/5)³ + (5²)⁵/² · (1/5)³ = 
= (5²)⁶ · 5³ · (1/5)³ + 5⁵ · (1/5)³ = 
= 5¹²⁺³ · (1/5)³ + 5⁵ · (1/5)³ = 
= 5¹⁵ · (1/5)³ + 5⁵ · (1/5)³ = 
= 5¹⁵⁻³ + 5⁵⁻³ = 
= 5¹² + 5²

7)(25⁴)¹/⁸ = (25)⁴/⁸ = 25¹/² = (5²)¹/² =5