2. a) [latex]sqrt{7^2}+sqrt6-(sqrt6)^2=7+sqrt6-6=1-sqrt6[/latex] b) [latex]sqrt[3]{12^3}-(sqrt{17})^2-sqrt5=12-17-sqrt5=-5-sqrt5=-(5+sqrt5)[/latex] c) [latex]3sqrt{5^2}+2sqrt5-2sqrt[3]{(-5)^3}=3cdot5+2sqrt5-2cdot(-5)=\ 15+10+2sqrt5=25+2sqrt5[/latex] d)[latex] -sqrt[3]{5^3}-sqrt[3]7-sqrt[3]{-7}=-5-sqrt[3]7-(-7)=-5+7-sqrt[3]7=2-sqrt[3]7[/latex] 4. a) [latex]sqrt{7^6}=sqrt{(7^3)^2}=7^3[/latex] [latex]sqrt{12^8}=sqrt{(12^4)^2}=12^4[/latex] b) [latex]sqrt[3]{5^{12}}=sqrt[3]{(5^4)^3}=5^4[/latex] [latex]sqrt[3]{12^9}=sqrt[3]{(12^3)^3}=12^3[/latex] c) [latex](sqrt8)^6=((sqrt{8})^2)^3=8^3[/latex] [latex](sqrt6)^{10}=((sqrt6)^2)^5=6^5[/latex] d) [latex](sqrt[3]{11})^{12}=((sqrt[3]{11})^3)^4=11^4[/latex] [latex](sqrt[3]{-9})^{21}=((sqrt[3]{-9})^3)^7=(-9)^7=-9^7[/latex]
