6.
По действиям:
1) (2 ¹/₄)⁻² = (⁹/₄)⁻² = (⁴/₉)² = 4²
9²
2) (25/81)^(0.5) = ((5/9)²)^(0.5)=5/9
3) (1/81)^0.25 = (3⁻⁴)^0.25=3⁻¹ =1/3
4) (1/32)^(-4/5)=32^(4/5)=(2⁵)^(4/5)=2⁴=16
5) (-6.8)⁰=1
6) 9 * 4² + 5 + 2 * 1 + 16*1 = 16 + 5 + 2 + 16= 21 + 2 + 16 =
9² 9 3 9 9 3 9 3
= 7 + 2 + 16 = 9 + 16 = 3+16 =19
3 3 3
Ответ: 19.
7. По действиям:
1) √[(4/49) * (2⁴/3²)] = √(4/49) * √(2⁴/3²) = 2 * 2² = 8
7 3 21
2) (99.32)⁰ = 1
21 21
3) (9^(1/8))^(-8/2) =9^(-1/2)=(3²)^(-1/2)=3⁻¹= 1
3
4) (1/27)^(-2/3)=(3⁻³)^(-2/3)=3⁻²= 1
9
5) (16/81)^(1/4)=((2/3)⁴)^(1/4)=2
3
6) (6/5)² = 36
25
7) (1/4)^(-1/2)=(2⁻²)^(-1/2)=2¹=2
8) (1/27)^(-1/3)=(3⁻³)^(-1/3)=3¹=3
9) 8 - 1 + 1 * 9 + 2 = 7 + 3 + 2 = 1 + 3 + 2 = 4*25 = 25 = 2 ⁷/₉
21 21 3 3 21 3 3 3 36 9
36 * (2*2-3) 36 36
25 25 25
Ответ: 2 ⁷/₉.
8. По действиям:
1) 3 : 1 = 3 * 8 = 3
8 8 8 1
2) 9^(-0.5)=(3²)^(-0.5)=3⁻¹= 1
3
3) 81^(-0.25)=(3⁴)^(-0.25)=3⁻¹ = 1
3
4) (7/10)⁰=1
5) 4⁻³ = 1 = 1
4³ 64
6) 3 - 1 : 1 + (1+2,6)⁰ =
(11 -64 * 1 ) *0,16 +0,4
64
= 2 + 1 = 2 + 1 =
(11-1)*0,16+0,4 10*0,16+0,4
= 2 +1 = 2
2
Ответ: 2.