Question

Calculati , folosind proprietatea a la m :a la n =a la m-n
a)8 la puterea 15:8 la puterea 12=
b)13 la puterea 31:13 la puterea 30+13=
c)7 la puterea 29:7 la puterea 26-7 la puterea 2=
d)7 la puterea 17:7 la puterea 13-7 la puterea 3+13 la puterea 0=
e)(11+4)la puterea 22:15 la puterea 20-15 la puterea 0=
f)(42:14)la puterea 2*9 la puterea 18:27 la puterea 6=
Va rog imi trebuie repede!!!!!

Answer 1

$a).8^1^5:8^1^2=8^{15-12}=8^3=512 \\ \\ b).13^3^1:13^3^0+13=13^{31-30}+13=13^1+13=13+13=26 \\ \\ c).7^2^9:7^2^6-7^2=7^{29-26}-49=7^3-49=343-49=294 \\ \\ d).7^1^7:7^1^3-7^3+13^0=7^{17-13}-7^3+1=7^4-7^3+1= \\ \\ =7^3(7-1)+1=7^3*6+1=343*6+1=2058+1=2059 \\ \\ e).(11+4)^2^2:15^2^0-15^0=15^2^2:15^2^0-1=15^{22-20}-1= \\ \\ =15^2-1=225-1=224$

$f).(42:14)^2*9^1^8:27^6=3^2*(3^2)^1^8:(3^3)^6=3^2*3^3^6:3^1^8= \\ \\ =3^2^+^3^6:3^1^8=3^3^8:3^1^8=3^{38-18}=3^2^0$

Answer 2

Trebuie să faci diferenţa dintre cele două puteri.
$8^{15} : 8^{12} = 8 x^{15-12} = 8^{3}$
$13^{31} : 13^{30} + 13= 13+13=26$
$7^{29} : 7^{26} - 7^{2}$ $= 7^{3} - 7^{2}$ =$7^{3} - 7^{2} =294$
[tex] 7^{17}: 7^{13} - 7^{3} + 1 = 7^{4}- 7^{3} +1= 2058 + 1= 2059 [/tex]
$15^{22} : 15^{20} -1= 15^{2} -1= 225-1=224$
$3^{2} * 3^{36}: 3^{18}= 3^{38} : 3^{18} = 3^{20}$