Question

Oblicz wartości wyrażeń:
a) (4a³)⁴ :( ¹₂ a²)³ dla a= - ¹₂
b) (25x²y²) :(5xy)³ dla x=-2 y=¹₅
c) (3ab² c³) * (5a² b² c²) dla a=0,1 b=10 c= -1
d) (7x⁶y⁵z⁴) : (5x⁴y³z²) dla x= -5 y=¹₇ z =-1
e) [2a²/ 3b³] * [3b⁴/2a²]⁴ dla a=½ b = -⅓

Answer 1

A)[(4*(-1/2)³]⁴÷[(½*(-½)²]³=(4*(-⅛)⁴÷(½*¼)³=(-½)⁴÷(⅛)³=1/16÷1/512=1/16*512=32
b)[25*(-2)²*⅕²]÷[5*(-2)*⅕]³=[25*4*1/25]÷[-10*⅕]³=100/25÷(-10/5)³=100/25÷(-1000/125)=-5/10=-1/2
c)[3*0,1*10²*(-1)³]*[5*(0,1)²*10²*(-1)²]=[0,3*100*(-1)]*[0,05*100*1]=(-30)*5=-150
d) [7*(-5)⁶*½⁵*(-1)⁴]÷[5*(-5)⁴*½³*(-1)²=[7*(-15625)*1/32*1]÷[5*625*1/8*1]=[-109375*1/32]÷[3125*1/8]=[-109375/32]÷[3125/8]=-109375/32*8/3125=-35/4
e)[2*½²/3*(-⅓)³]*[3*(-⅓)⁴/2*½²]⁴=[2*¼/3*(-1/27)]*[3*1/81 / 2*¼]=[½/-1/9]*[1/27 / ½]=[½÷(-1/9)]*[1/27÷1/2]=[1/2*(-9)]*[1/27*2]=-9/2*2/27=-18/54=-1/3