1) 12⁻³=1/12³=1/1728
2) 3⁻⁴=1/3⁴=1/81
3) (-2)⁻⁶=1/(-2)⁶=1/64
4) (-5)⁻³=-1/5³=-1/125
5) 100⁻¹=1/100=0,01
6) (-1/8)⁻¹=-8
7) (2/3)⁻³=(3/2)³=27/8=3 3/8
8) (-7/9)⁻²=(9/7)²=81/49=1 32/49
9) (1 2/3)⁻¹=(5/3)⁻¹=3/5=0,6
10) (-1 1/4)⁻³=(-5/4)⁻³=(-4/5)³=-64/125
11) (0,01)⁻³=(1/100)⁻³=100³=1 000 000
12) (1,6)⁻²=(1 3/5)⁻²=(8/5)⁻²=(5/8)²=25/64
1) 3⁻³ + 6⁻² = 1/27 + 1/36 = 4/108 + 3/108 = 7/108
2) (2/3)⁻¹ + (-1,7)⁰ - 2⁻³ = 3/2 + 1 - 1/8 = 12/8 + 1 - 1/8 = 11/8 + 8/8 = 19/8 = 2 3/8
3) (3/4)⁻² * 2⁻³ = 16/9 * 1/8 = 16/(9*8) = 2/9
4) 10⁻¹ + 5⁻² - 2⁻³ = 1/10 + 1/25 - 1/8 = 20/200 + 8/200 - 25/200 = 3/200 = 15/1000 = 0,015
= 1/√((1-2x)/(1+2x)) * (1/2√(1-2x)/(1+2x))*(-2)(1+2x)-2(1-2x)/(1+2х)²=
= 1/√((1-2x)/(1+2x)) * (1/2√(1-2x)/(1+2x))* (-2-4х-2 +4х)/(1+2х)²=
=- 1/√((1-2x)/(1+2x)) * (1/2√(1-2x)/(1+2x))*4/(1+2х)²
2)у = √х*Cosx
y'=1/2√x*Cosx - √x*Sinx
3) f(x) = e^Sin4x
f'(x) = e^Sin4x * Cos4x*4
f'(0)= e^0*Cos0*4 = 1*1*4 = 4
4) f(x) (3x-4)*ln(3x-4)
f'(x) =3*ln(3x-4) + (3x-4)*3/(3x-4)= 3ln(3x-4) +3
5)f(x)=5^lnx
f'(x) = 5^lnx*1/x*ln5
6) f(x) = Ctg(2x + π/2) + (x-π²)/х = -tg2x + (x-π²)/х
f'(x) = -2/Cos²2x + (x - x + π²)/х² = -2/Cos² 2x + π²/x²
f'(π/12) = -2/Сos² π/6 + π²/π/12 = -3/2 + 12π