Question

Answer 1

a) \(4^8.2^{20}=\left(2^2\right)^8.2^{20}=2^{16}.2^{20}=2^{36}\)

b) \(25^{20}.125^4=\left(5^2\right)^{20}.\left(5^3\right)^4=5^{40}.5^{12}=5^{52}\)

c) \(9^{12}.27^5.81^4=\left(3^2\right)^{12}.\left(3^3\right)^5.\left(3^4\right)^4=3^{24}.3^{15}.3^{16}=3^{55}\)

d) \(x^7.x^4.x^3=x^{14}\)

e) \(27^6:9^3=\left(3^3\right)^6:\left(3^2\right)^3=3^{18}:3^6=3^{12}\)

f) \(4^{20}:2^{15}=\left(2^2\right)^{20}:2^{15}=2^{40}:2^{15}=2^{25}\)

g) \(4^{10}:64^3=4^{10}:\left(4^3\right)^3=4^{10}:4^9=4\)

h) \(5^9:25^3=5^9:\left(5^2\right)^3=5^9:5^6=5^3\)

i) \(3^6.4^6=\left(3.4\right)^6=12^6\)

k) \(18^{10}:3^{10}=\left(18:3\right)^{10}=6^{10}\)

m) \(48^n:4^{2n}=48^n:\left(4^2\right)^n=48^n:16^n=\left(48:16\right)^n=3^n\)

n) \(64^4.16^5:4^{20}=\left(4^3\right)^4.\left(4^2\right)^5:4^{20}=4^{12}.4^{10}:4^{20}=4^2\)

p) \(\left(ab\right)^6:b^6=a^6.b^6:b^6=a^6\)

q) \(27^3.9^4.243=\left(3^3\right)^3.\left(3^2\right)^4.3^5=3^9.3^8.3^5=3^{22}\)

o) \(8^2.32^4.\left(2^4\right)^2=\left(2^3\right)^2.\left(2^5\right)^4.\left(2^4\right)^2=2^6.2^{20}.2^8=2^{34}\)

Answer 2

a) 48.220=(22)8.220=216.220=23648.220=(22)8.220=216.220=236

b) 2520.1254=(52)20.(53)4=540.512=5522520.1254=(52)20.(53)4=540.512=552

c) 912.275.814=(32)12.(33)5.(34)4=324.315.316=355912.275.814=(32)12.(33)5.(34)4=324.315.316=355

d) x7.x4.x3=x14x7.x4.x3=x14

e) 276:93=(33)6:(32)3=318:36=312276:93=(33)6:(32)3=318:36=312

f) 420:215=(22)20:215=240:215=225420:215=(22)20:215=240:215=225

g) 410:643=410:(43)3=410:49=4410:643=410:(43)3=410:49=4

h) 

i) 

k) 1810:310=(18:3)10=6101810:310=(18:3)10=610

m) 48n:42n=48n:(42)n=48n:16n=(48:16)n=3n48n:42n=48n:(42)n=48n:16n=(48:16)n=3n

n) 644.165:420=(43)4.(42)5:420=412.410:420=42644.165:420=(43)4.(42)5:420=412.410:420=42

p) 

q) 273.94.243=(33)3.(32)4.35=39.38.35=322273.94.243=(33)3.(32)4.35=39.38.35=322

o) 82.324.(24)2=(23)2.(25)4.(24)2=26.220.28=234