1. a) 6^15 *6^(-13) =6^(15+(-13)) =6² =36
или
6^15/6^13 =6² =36
b) 4^-6 /4^-3 =4^3/4^6 =1/4^3 =1/64
(1/x^-1 =x^1, x^-1 =1/x)
в) (5^-1)^3 =(1/5)^3 =1/125 =0.008
2. a) (x-²)^-4 *x^-7 =(1/x²)^-4 *x^-7 =(x²)^4 /x^7 =x^8 /x^7 =x
b) =(1.2b^8 *5a^6) /(a^5*b^6) =6ab²
3. a) =(2/3a^4b²)-² =(3a^4b² /2)² =(9a^6b^4)/4 =2.25a^6b^4
b) =(5b/6a²)-² *10a^3b^4 =(6a²/5b)² *10a^3b^4 =(36a^4*10a^3b^4)/25b² =(36*2a^7b²)/5 =14.4a^7b²
4. (5^-9 *25-²)/125^-4 =125^4/(5^9 *25²) =5^12 /(5^9 *5^4) =5^12 /5^13 =1/5 =0.2
5. (a^-1 +b)(a +b^-1)^-1 =(1/a +b) *(a +1/b)^-1 =(1+ab)/b *(ab+1)/b)^-1 =(1+ab)/b *b/(ab+1) =(1+ab)*b /b*(1+ab) =1