19. a) 2^11(1+1)=2^11•2=2^12
б) 3^7(1+1+1)=3^7•3=3^8
в) 3^9(5–2)=3^9•3=3^10
г) 2^5(9–1)=2^5•8=2^5•2^3=2^8
20. 4^14 4^14
а) ------------ = -------- = 4
4^3•4^10 4^13
3^4•3^5 3^9
б) ------------- = ------ = 3^2 = 9
3^7 3^7
2^7•3^9
в) ------------- = 2^2•3^4 = 4•81 = 324
3^5•2^5
21. х^(n+m) x^(n+m)
a) -------------------- = ----------------- = 1
x^(n+1)•x^(m-1) x^(n+1+m–1)
а^(2+n+1+3)
б) ------------------ = a^(6+n–n–5) = a
a^(n-1+6)
х^(2n+n+3)
в) ----------------- = x^(3n+3–3n) = x^3
x^3n
d^(n+1) 1
г) --------------- = d^(n+1–n–2) =d^-1= ---
d^(n–5+7) d
22. 2^n(2^2+1+1+1+1) 8
а) ------------------------- = ----- = 1
2^n(2^3) 2^3
3^n(3^2+5)
б) ----------------- = 9+5 = 14
3^n
5^n(5^1–1)
в) ---------------- = 5–1 = 4
5^n
4^n(4^1+4^2)
г) ------------------- = 4+16 = 20
4^n
2^n(2^3–2^1) 8–2 6
д) -------------------- = ------ = --- = 2
2^n(2^1+1) 2+1 3
3^n(3^3–3^1+1) 27–3+1 25
e) ---------------------- = ----------- = ----
3^n(3^2+3^1) 9+3 12