Question

Calculati:a)7la puterea2:{17la puterea2:289+2x[(2la puterea3x3)la puterea13:(2x2la puterea43x3la puterea15)+1la puterea100]};b)5la puterea140:25la
puterea70+8la puterea32:16la puterea24+100la puterea25:10la puterea48-2la puterea2x5la puterea2;c)[3la puterea100:3la puterea10+(9la puterea5x3la puterea14)la puterea5:27la puterea10+(4la puterea30:4la puterea29-1la puterea20)la puterea102:81la puterea3]:(2la puterea10:2la puterea9+1)la puterea90.d)3la puterea61:(3la puterea4)la puterea15+(5la puterea2)la puterea3:5la puterea2(iar puterea2 este la randul ei la puterea0).e)2x2la puterea2x2la puterea3+10.va rog frumos sa ma ajutati!

Answer 1

a)7^2:{17^2:289+2x[(2^3x3)^13:(2x2^43x3^15)+1^100]}=
=7^2:{17^2:17^2+2x[(2^39x3^13:(2^44x3^15)+1]}=
=7^2:{1+2x[(2^39x3^13:(2^44x3^15)+1]}=
=7^2:{1+2x[(1:(2^5x3^2)+1]}=
=7^2:{1+2x[(1:288+1]}=
=7^2:{1+2x289/288}=
=7^2:{1+289/144}=
=7^2:(144+289)/144=
=7^2:433/144=
=49x144/433=7056/433  

b)5^140:25^70+8^32:16^24+100^25:10^48-2^2x5^2=
=5^140:5^140+2^96:2^96+10^50:10^48-2^2x5^2=
=1+1+10^2-10^2=2


c)[3^100:3^10+(9^5x3^14)^5:27^10+(4^30:4^29-1^20)^102:81^3]:(2^10:2^9+1)^90=
=[3^90+(3^10x3^14)^5:3^30+(2^60:2^58-1)^102:3^12]:(2+1)^90=
=[3^90+(3^24)^5:3^30+(2^2-1)^102:3^12]:(2+1)^90=
=[3^90+3^120:3^30+3^102:3^12]:3^90=
=[3^90+3^90+3^90]:3^90=
=1+1+1=3

d)3^61:(3^4)^15+(5^2)^3:5^2^0=
=3^61:3^60+5^6:5^1=
=3+5^5=
=3+3125=3128

e)2x2^2x2^3+10=
=2^6+10=
=64+10=74