\(x.x^2.x^3...x^{49}=x^{1+2+3+...+49}=x^{1225}\)

a: \(4^8\cdot2^{20}=\left(2^2\right)^8\cdot2^{20}=2^{16}\cdot2^{20}=2^{16+20}=2^{36}\)

\(9^{12}\cdot27^5\cdot81^4=\left(3^2\right)^{12}\cdot\left(3^3\right)^5\cdot\left(3^4\right)^4\)

\(=3^{24}\cdot3^{15}\cdot3^{16}=3^{24+15+16}=3^{55}\)

\(64^3\cdot4^5\cdot16^2=\left(4^3\right)^3\cdot4^5\cdot\left(4^2\right)^2=4^9\cdot4^5\cdot4^4=4^{9+5+4}=4^{18}\)

b: \(25^{20}\cdot125^4=\left(5^2\right)^{20}\cdot\left(5^3\right)^4=5^{40}\cdot5^{12}=5^{52}\)

\(x^7\cdot x^4\cdot x^3=x^{7+4+3}=x^{14}\)

\(3^6\cdot4^6=\left(3\cdot4\right)^6=12^6\)

c: \(8^4\cdot2^3\cdot16^2=\left(2^3\right)^4\cdot2^3\cdot\left(2^4\right)^2\)

\(=2^{12}\cdot2^3\cdot2^8=2^{23}\)

\(y\cdot y^7=y^{1+7}=y^8\)

\(2^3\cdot2^2\cdot8^3=2^5\cdot\left(2^3\right)^3=2^5\cdot2^9=2^{5+9}=2^{14}\)

a,  4 8 . 4 10 = 4 18

b,  2 20 . 2 7 = 2 27

c,  5 12 . 5 5 . 5 4 = 5 21

d,  4 3 . 4 5 . 4 5 = 4 13

e,  8 6 . 8 5 . 8 5 = 8 16

f,  x 7 . x 4 . x 3 = x 14

\(a,4^8.2^{20}=\left(2^2\right)^8.2^{20}=2^{16}.2^{20}=2^{16+20}=2^{36}\\ b,9^{12}.27^5.81^4=\left(3^2\right)^{12}.\left(3^3\right)^5.\left(3^4\right)^4=3^{24}.3^{15}.3^{16}=3^{24+15+16}=3^{55}\\ d,25^{20}.125^4=\left(5^2\right)^{20}.\left(5^3\right)^4=5^{40}.5^{12}=5^{40+12}=5^{52}\\ d,x^7.x^4.x^3=x^{7+4+3}=x^{14}\)

a: 4*8*2^20=2^2*2^3*2^20=2^25

b: 9^12*27^5*81^4=3^24*3^15*3^16=3^55

c: 25^20*125^4=5^40*5^12=5^52

d: =x^(7+4+3)=x^14