Question

va rog exercitiul 1 ,2 si 7 dau mai mult de 30 de puncte si o coroana

Answer 1

1. a) $4^{17} = (2^{2})^17= 2^{34}$
b).$3^{27} \ \textgreater \ 3^{26}$
c)$49^{18} = (7^{2})^18= 7^{36} \ \textgreater \ 7^{35}$
d)$2^{51} \ \textgreater \ 2^{52}$
e)[te] 64^{17}= (8^{2} )^17= 8^{34} [/tex]
g)$100^{10} = (10^{2})^10= 10^{20} \ \textless \ 10^{100}$). 
3. a) $2^{35} = 2^{35}$
[tex] 4^{18} = (2^{2})^18= 2^{36}
   8^{11}= (2^{3})^11 = 2^{33}
 8^{11} \ \textless \ 2^{35} \ \textless \ 4^{18} [/tex]
c) $5^{39} \ \textless \ 25^{20} \ \textless \ 125^{14}$
7. b) y=8x(7+5-4)=$8^{2}= 4^{3}$
c) z=27x(95-68)=$27^{2}= 3^{6}= (3^{2})^3= 9^{3}$
f). v=$2^{61}- 2^{60} = (2^{30)^2}= (2^{20})^3$
g). w=$3^{37}-2x 3^{36}= (3^{18})^2= (3^{12})^3$
i). r=$( 6^{7})^8 : 6^{2} = 6^{56} : 6^{2} = 6^{54} = (6^{18})^3$

Answer 2

1.
__a) 4$4^{17}$=(2²)$^{17}$=$2^{34}$⇒$4^{17}$=$2^{34}$

__b)$9^{13} =(9^2)^13$$= 3^{26}$⇒$3^{27}$≥$9^{13}$

__c)$49^{18} =(7^2)^18$=$7^{36}$⇒$49^{18} \geq 7 ^{35}$

__d)$8^{17} =(2^{3} ) ^{17}$=$8^{51}$⇒$8^{17} \leq 2 ^{52}$

__e)$64^{17} =( 8^{2}) ^{17} =8^{34}$⇒$63^{17} =8^{34}$

__f)$81^{25} =(3^{4})^{25}=3^{100}$⇒ $81^{25}$ $3^{100}$
 
__g)$100^{10} = (10^{2})^{10}=10^{20}$⇒$100^{10} \leq 10^{100}$

_h)$27^{13} =(3^{3})^{13}=3^{39} ; 9^{20} =( 3^{2})^{20}=3^{60}$ ⇒