[tex]\displaystyle d)2^1\cdot2^2\cdot...\cdot2^{20}=2^{1+2+...+20}=2^{\frac{20(20+1)}{2}}=2^{\frac{20\cdot21}{2}}=2^{\frac{420}{2}} =2^{210}\\ \\ e)4^1\cdot4^2\cdot...\cdot4^{50}=4^{1+2+3+...+50}=4^{\frac{50(50+1)}{2}}=4^{\frac{50\cdot51}{2}}=4^{\frac{2550}{2}}=4^{1275}=2^{2550}\\ \\ f)2^{80}:2^{35}:2^{10}=2^{80-35-10}=2^{35}\\ \\ g)7^{20}:7^{10}:7^5=7^{20-10-5}=7^5\\ \\ h)9^{120}:9^{20}:9^{50}=9^{120-20-50}=9^{50}=3^{100}\\ \\ i)(2^2)^7\cdot2^{10}:(2^4)^6=2^{14}\cdot 2^{10}:2^{24}=2^{14+10-24}=2^0=1[/tex]
[tex]\displaystyle j)(3^4)^{20}:(3^2)^{10}:3^{50}=3^{80}:3^{20}:3^{50}=3^{80-20-50}=3^{10}\\ \\ k)[(2^3)^4]^5:2^{50}=(2^{12})^5:2^{50}=2^{60}:2^{50}=2^{60-50}=2^{10}\\ \\ l)[(3^5)^{10}]^2:(3^4)^{20}=(3^{50})^2:3^{80}=3^{100}:3^{80}=3^{100-80}=3^{20}\\ \\ m)2^7\cdot2^9\cdot2^3:2^8:2^{10}=2^{7+9+3-8-10}=2^1=2\\ \\ n)3\cdot3^{14}\cdot3^2:3^{16}=3^{1+14+2-16}=3^1=3\\ \\ k)(5^3\cdot5^8):(5^3\cdot5^7)=5^{3+8}:5^{3+7}=5^{11}:5^{10}=5^{11-10}=5^1=5[/tex]
