Question

a) 3^{-2} * \frac{2}{3} - (\frac{9}{8})^{-1} =

b) (0,2)^{2} * 5^{-3}

--------------------- =

10^{-3} : (0,1)^{-2}

Answer 1

a) 3^{-2} * 2/3 - (9/8)^{-1} = (1/3)^2  * 2/3 - (8/9)^1  = 1/9 * 2/3 - 8/9 = 2/27 - 8/9 =

2/27 - 24/27 = - 22/27

 

b) (0,2)^{2} * 5^{-3}          0,04 * (1/5)^3    0,04 * 1/125       4/100 * 1/125

   ---------------------      = ------------------ = ---------------- = ----------------- =

   10^{-3} : (0,1)^{-2}        10^(-3) : 10^2       10^(-3 - 2)         10^(-5)

 

4/12500 : (1/10)^5 = 4/12500 : 1/100000 = 4/12500 * 100000/1 = 4 000/125 = 32