How do you simplify #sqrtx^(2n)* sqrty^(2n +1)#? Algebra Radicals and Geometry Connections Multiplication and Division of Radicals 1 Answer LM Oct 18, 2017 #x^n * y^(n+0.5)# Explanation: laws of indices: #rootna = a^(1/n)# #(a^m)^n = a^(mn)# #a^m * a^n = a^(m+n)# and in practice: #sqrt(x) = x^(1/2)# #sqrt(x) ^(2n) = (x^(1/2))^(2n)# #(x^(1/2))^(2n) = x^(1n) = x^n# #sqrt(y) ^(2n+1) = (y^(1/2))^(2n+1)# #(y^(1/2))^(2n+1) = y^(n+0.5)# #y^(n+0.5) = y^n * y^0.5 = sqrty *y^n# #sqrtx^(2n)⋅sqrty^(2n+1) = x^n * sqrty *y^n# #x^n * y^(n+0.5)# Answer link Related questions How do you simplify #\frac{2}{\sqrt{3}}#? How do you multiply and divide radicals? How do you rationalize the denominator? What is Multiplication and Division of Radicals? How do you simplify #7/(""^3sqrt(5)#? How do you multiply #(sqrt(a) +sqrt(b))(sqrt(a)-sqrt(b))#? How do you rationalize the denominator for #\frac{2x}{\sqrt{5}x}#? Do you always have to rationalize the denominator? How do you simplify #sqrt(5)sqrt(15)#? How do you simplify #(7sqrt(13) + 2sqrt(6))(2sqrt(3)+3sqrt(6))#? See all questions in Multiplication and Division of Radicals Impact of this question 916 views around the world You can reuse this answer Creative Commons License