Autorzy:Drążek Anna, Duvnjak Ewa, Kokiernak-Jurkiewicz Ewa
Wydawnictwo:WSiP
Rok wydania:2016
Oblicz. a) 4*(-2 ¼)⁸*(1/9)⁸4.43 gwiazdek na podstawie 7 opinii

a)

Ze względu na złożoność obliczeń upraszczamy najpierw osobno licznik i mianownik ułamka.

`4*(-2 1/4)^8*(1/9)^8+(1/4)^12:(-1/4)^4*5=4*(-9/4)^8*(1/9)^8+(1/4)^12:(-1/4)^4*5=`

`=4*(-9/4*1/9)^8+(1/4)^12:((-1)^4*(1/4)^4)*5=4*(-1/4)^8+(1/4)^12:(1/4)^4*5=`

`=4*((-1)^8*(1/4)^8)+(1/4)^(12-4)*5=4*(1/4)^8+5*(1/4)^8=9*(1/4)^8`

 

`(-1,25)^6*(1/5)^6*0,15=(-1 25/100)^6*(1/5)^6*15/100=`

`(-1 1/4)^6*(1/5)^6*3/20=(-5/4)^6*(1/5)^6*3/20=(-5/4*1/5)^6*3/20=`

`(-1/4)^6*3/20=((-1)^6*(1/4)^6)*3/20=(1/4)^6*3/20` 

 

 

 

` (4*(-2 1/4)^8*(1/9)^8+(1/4)^12:(-1/4)^4*5)/((-1,25)^6*(1/5)^6*0,15)=(9*(1/4)^8)/((1/4)^6*3/20)=`

`(9*(1/4)^6*(1/4)^2)/((1/4)^6*3/20)=(9*(1/4)^2)/(3/20)=(9*1/16):3/20=9/16*20/3=3/4*5/1=15/4=3 3/4`

 

b)

`-7*[(-3/5)^18:(0,3)^17]-0,2*(1/2)^17:(-1/4)^18=-7*[((-1)^18*(3/5)^18:(3/10)^17)]-2/10*(1/2)^17:((-1)^18*(1/4)^18)=`

`=-7*[(3/5)^18*(10/3)^17]-2/10*(1/2)^17:(1/4)^18=-7*[(3/5*(3/5)^17*(10/3)^17]-2/10*(1/2)^17*(4/1)^18=`

`=-7*[3/5*(3/5*10/3)^17]-2/10*(1/2)^17*4^17*4=-7*[3/5*(10/5)^17]-2/10*(1/2*4)^17*4=`

`=-7*3/5*(10/5)^17-2/10*(4/2)^17*4=-21/5*2^17-8/10*2^17=-21/5*2^17-4/5*2^17=-25/5*2^17=-5*2^17`

 

`0,4*(-2)^8*(-2)^7+(-2)^14=0,4*(-2)^(8+7)+(-2)^14=0,4*(-2)^15+(-2)^14=0,4*(-2)*(-2)^14+(-2)^14=`

`=-0,8*(-2)^14+(-2)^14=(-2)^14*(-0,8+1)=0,2*(-2)^14=0,2*(-1)^14*2^14=0,2*2^14` 

 

 

 

 

` (-7*[(-3/5)^18:(0,3)^17]-0,2*(1/2)^17:(-1/4)^18)/(0,4*(-2)^8*(-2)^7+(-2)^14)=(-5*2^17)/(0,2*2^14)=`

`=(-5*2^17)/(2/10*2^14)=-5*2^17:(1/5*2^14)=-5*5/1*2^(17-14)=-25*2^3=-25*8=-200`