Question

efectuati:a)6 la puterea 4 -5 la puterea :b)49 la puterea 1 - 1 la puterea 49:c) 45 la puterea 2*2 la puterea 2:d) (3 la puterea 2*3)la puterea 2

Answer 1

a)6^4 -5^????
b)49^1 - 1^49=49-1=48
c) 45^2*2^2 =2025*4=8100
d) (3^2*3)^2 =27^2=729

Comparati numerele:
a)91^53 < 91^62
b)24^125 > 23^125
c)19^34 > 9^32
d)2^55 > 5^22
(2^5)^11 =32^11
(5^2)^11=25^11


a) 12^55:6^55:2^50 - 7^1*5^0 + 13^2=
=2^55:2^50 - 7 + 169=
=2^5 - 7 + 169=
=32+162=194

b) (2*5)^3 + 45^45:9^45:5^44-2000^0=
=2^15 + 3^90*5^45:3^90:5^44-1=
=2^15 + 5-1=
=2^15+2^2=
=2^2(2^13+1)
=4*(8192+1)=
=32772

d=(4^50+4^49 + 4^48):21 =
=4^48(4^2+4^1 + 1):21 =
=4^48(16+4 + 1):21 =
=4^48 *21:21
=4^48
(2^48)^2 deci este patrat perfect
4^48=(4^16)^3  deci este cub perfect


s=8 la puterea 283+9 la puterea 216  se termina in 2+9=11 deci in 1
8^283 se termina ca 8^3 deci in 2
283:4=70 si rest 3

9^216 se termina ca 9^1 deci in  9
283:2=141 si rest 1

9^(x + 2) +9^(x + 1) + 9^x=91*3^28
9^x(9^2 +9^1 + 9^0)=91*3^28
9^x(81+9+1)=91*3^28
9^x *91=91*3^28
3^2x =3^28
2x=28
x=14