Question 353584
First one: You have an addition error somewhere. The answer should be {{{highlight_green(11/(z+9))}}}.
Check your work to see if you can spot the error.
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{{{(5*sqrt(2) - 10*sqrt(5))(3*sqrt(2) + 6*sqrt(5))}}}
Use the FOIL method,
{{{(5*sqrt(2) - 10*sqrt(5))(3*sqrt(2) + 6*sqrt(5))=15*2+30*sqrt(10)-30*sqrt(10)-60*5}}}
{{{(5*sqrt(2) - 10*sqrt(5))(3*sqrt(2) + 6*sqrt(5))=30-300}}}
{{{(5*sqrt(2) - 10*sqrt(5))(3*sqrt(2) + 6*sqrt(5))=highlight(-270)}}}
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{{{root(3,(y^7))*root(3,(16y^8))=root(3,(16*y^(7+8)))}}}
{{{root(3,(y^7))*root(3,(16y^8))=root(3,(16*y^(15)))}}}
{{{root(3,(y^7))*root(3,(16y^8))=root(3,(2*8*y^(15)))}}}
{{{root(3,(y^7))*root(3,(16y^8))=root(3,(2))*root(3,8y^(15))}}}
{{{root(3,(y^7))*root(3,(16y^8))=highlight_green(2y^5*root(3,(2)))}}}