1a) (3⁻³)⁻¹ = 3³ = 27
1б) 11¹² * 11⁻¹⁰ = 11¹²⁺⁽⁻¹⁰⁾ = 11¹²⁻¹⁰ = 11² = 121
1в) 8⁻⁸ : 8⁻⁷ = 8⁻⁸⁻⁽⁻⁷⁾ = 8⁻⁸⁺⁷ = 8⁻¹ = 0,125
2a) 3,6a⁻⁷b¹⁰ * 5a⁹b⁻⁸ = 3,6 * 5 * a⁻⁷⁺⁹b¹⁰⁻⁸ = 18a²b²
2б)
![(\frac{5x^{2}}{3y^{3}})^{-2}*100x^{7}y^{4}=\frac{9y^{6}}{25x^{4}}*100x^{7}y^{4}=36x^{3}y^{10} (\frac{5x^{2}}{3y^{3}})^{-2}*100x^{7}y^{4}=\frac{9y^{6}}{25x^{4}}*100x^{7}y^{4}=36x^{3}y^{10}](https://tex.z-dn.net/?f=%28%5Cfrac%7B5x%5E%7B2%7D%7D%7B3y%5E%7B3%7D%7D%29%5E%7B-2%7D%2A100x%5E%7B7%7Dy%5E%7B4%7D%3D%5Cfrac%7B9y%5E%7B6%7D%7D%7B25x%5E%7B4%7D%7D%2A100x%5E%7B7%7Dy%5E%7B4%7D%3D36x%5E%7B3%7Dy%5E%7B10%7D)
3a) 8400 = 8,4 * 10³
3б) 0,076 = 7,6 * 10⁻²
3в) 542,7 * 10⁴ = 5,427 * 10² * 10⁴ = 5,427 * 10⁶
3г) 317 * 10⁻³ = 3,17 * 10² * 10⁻³ = 3,17 * 10⁻¹
4)
![\frac{x^{-1}+y^{-1}}{(x+y)^{2}}=\frac{\frac{1}{x}+\frac{1}{y}}{(x+y)^{2}}=\frac{x+y}{xy(x+y)^{2} }=\frac{1}{xy(x+y)} \frac{x^{-1}+y^{-1}}{(x+y)^{2}}=\frac{\frac{1}{x}+\frac{1}{y}}{(x+y)^{2}}=\frac{x+y}{xy(x+y)^{2} }=\frac{1}{xy(x+y)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B-1%7D%2By%5E%7B-1%7D%7D%7B%28x%2By%29%5E%7B2%7D%7D%3D%5Cfrac%7B%5Cfrac%7B1%7D%7Bx%7D%2B%5Cfrac%7B1%7D%7By%7D%7D%7B%28x%2By%29%5E%7B2%7D%7D%3D%5Cfrac%7Bx%2By%7D%7Bxy%28x%2By%29%5E%7B2%7D%20%7D%3D%5Cfrac%7B1%7D%7Bxy%28x%2By%29%7D)