Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. √(96x^2y) Rewrite without rational exponents, and simplify, if possible. ( x^(4)…

Question

Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. 


`√(96x^2y)`




Rewrite without rational exponents, and simplify, if possible. 


`( x^(4) y^(4) )^(1/3)`

Answer 1

`√(96x^2y)=√(16\cdot6\cdot x^2\cdot y)=√(16)\cdot\sqrt6\cdot√(x^2)\cdot√(y)\\\\=4\cdot\sqrt6\cdot x\cdot√(y)=4x√(6y)`

========================================================


`\left(x^4y^4\right)^(1)/(3)=\left(x^4\right)^(1)/(3)\left(y^4\right)^(1)/(3)=x^{4\cdot(1)/(3)}y^{4\cdot(1)/(3)}=x^(4)/(3)y^(4)/(3)=x^{1+(1)/(3)}y^{1+(1)/(3)}\\\\=x^1x^(1)/(3)y^1y^(1)/(3)=x\sqrt[3]{x}\cdot y\sqrt[3]y=xy\sqrt[3]{xy}`