Question

1)2la17 •2la21 2)3la45•3la87•3la55 c)7la19•7la83•7 d)2la47:2la39 e)5la108:5la72
G)(10la12)15 h)(2la17)8•2la31 I)3la108:(3la15)6 j)(3la7•5la12)2

Answer 1

a) $2 ^{17} *2 ^{21} =2^{17+21}=2^{38}$

b)$3 ^{45} *3 ^{87}*3 ^{55} =3^{45+87+55}=3^{187}$

c)$7 ^{19} *7 ^{83} *7=7^{19+83+1}=7^{103}$

d)$2 ^{47} :2 ^{39} =2^{47-39}=2^{8}$

e)$5 ^{108} :5 ^{72} =5^{108-72}=5^{36}$

g)$(10 ^{12}) ^{15} =5^{12*15}=5^{180}$

h)$(2 ^{17}) ^{8}*2 ^{31} =2^{17*8}*2 ^{31}=2^{136}*2 ^{31}=2 ^{136+31}=2 ^{167}$

i)$3 ^{108}:(3 ^{15})^{6} =3^{108} :3^{15*6} = 3^{108}:3^{90}=3^{108-90}=3^{18}$

j)$(3^{7} * 5^{12} ) ^{2}= (3^{7})^{2} *( 5^{12} ) ^{2}=3^{7*2}*5^{12*2}=3^{14}*5^{24}$