150k views
0 votes
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)

1 Answer

1 vote

√(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}
User Victor Gallet
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories