[tex]a)~~(\dfrac{1}{42})^3:(-\dfrac{1}{21})^3-100^3\cdot(-\dfrac{1}{10})^3(\dfrac{1}{42}:(-\dfrac{1}{21}))^3-(100\cdot(-\dfrac1{10}))^3=\\=(-2)^3-(-10)^3=-8-(-1000)=-8+1000=992[/tex]
[tex]b)~~(1,2)^3:12^3-(0,6)^5\cdot(-1\dfrac23)^5=(1,2:12)^3-(0,6\cdot(-1\dfrac23))^5=\\=0,1^3-(\dfrac35\cdot(-\dfrac{5}{3}))^5=0,001-(-1)^5=0,001-(-1)=0,001+1=1,001[/tex]
[tex]c)~~-(-27)^3\cdot(-\dfrac19)^3-12^3:(-3)^3=-(-27\cdot(-\dfrac19))^3-(12:(-3))^3=\\=-3^3-(-4)^3=-27-(-64)=-27+64=37[/tex]
[tex]d)~~(-2\dfrac23)^{15}\cdot0,375^{15}+(-\dfrac23)^2\cdot0,75^2=(-2\dfrac23\cdot0,375)^{15}+(-\dfrac23\cdot0,75)^2=\\=(-\dfrac83\cdot\dfrac38)^{15}+(-\dfrac23\cdot\dfrac34)^2=(-1)^{15}+(-\dfrac12)^2=-1+\dfrac14=-\dfrac34[/tex]
