b) [tex][ \sqrt{10}-(-2 \sqrt{10}) ^{3} ]:(-9 \sqrt{5})=[ \sqrt{10}-(-8*10 \sqrt{10}) ]:(-9 \sqrt{5})= [/tex][tex][ \sqrt{10}-(-80 \sqrt{10}) ]:(-9 \sqrt{5})=[ \sqrt{10}+80 \sqrt{10} ]:(-9 \sqrt{5})= [/tex][tex]81 \sqrt{10}:(-9 \sqrt{5})=-9 \sqrt{2} [/tex]
c) [tex](-5 \sqrt{2})*| \sqrt{3}-(- \sqrt{6}) ^{3}:(-3 \sqrt{2})|=(-5\sqrt{2})*|\sqrt{3}- \sqrt{6} ^{3}:(3 \sqrt{2})|= [/tex][tex](-5\sqrt{2})*|\sqrt{3}- \frac{\sqrt{6} ^{3}}{3 \sqrt{2}}|=(-5\sqrt{2})*|\sqrt{3}- \frac{6\sqrt{6} }{3 \sqrt{2}}|=(-5\sqrt{2})*|\sqrt{3}-2 \sqrt{3}|= [/tex][tex](-5 \sqrt{2})*|- \sqrt{3}|=(-5 \sqrt{2}) \sqrt{3}=-5 \sqrt{2*3}=-5 \sqrt{6} [/tex]
d) [tex]|(- \sqrt{2}) ^{3}+(- \sqrt{2}) ^{5}|*(-2 \sqrt{6})=|- \sqrt{2} ^{3}- \sqrt{2} ^{5}|*(-2 \sqrt{6})= [/tex][tex]|- \sqrt{2 ^{3}}- \sqrt{2 ^{5}}|*(-2 \sqrt{6})=|-2 \sqrt{2}-2 ^{2}* \sqrt{2}|*(-2 \sqrt{6})= [/tex][tex]|-2 \sqrt{2}-4 \sqrt{2}|*(-2 \sqrt{6})= |-6 \sqrt{2}|*(-2 \sqrt{6})=6 \sqrt{2}*(-2 \sqrt{6})= [/tex][tex]-12 \sqrt{2*6}=-12 \sqrt{12}=-12 \sqrt{ 2^{2}*3 }=-12 \sqrt{ 2^{2} } \sqrt{3}=-12*2 \sqrt{3}= [/tex][tex]-24 \sqrt{3}[/tex]
e) [tex]|-21 \sqrt{40}|*[40 \sqrt{2}+(-3 \sqrt{2}) ^{3}]= |-42 \sqrt{10}|*[40 \sqrt{2}-27*2 \sqrt{2}]= [/tex][tex]42 \sqrt{10}*[40 \sqrt{2}-54 \sqrt{2}]=42 \sqrt{10}*[-14 \sqrt{2}]=-588 \sqrt{10*2}=[/tex][tex]-588 \sqrt{20} =-588 \sqrt{2 ^{2}*5 }=588 \sqrt{2 ^{2} } \sqrt{5}=-588*2 \sqrt{5}=-1176 \sqrt{5} [/tex]
