How do you simplify #sqrtx^(2n)* sqrty^(2n +1)#?

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Answer 1 · 2017-10-18T21:06:48

#x^n * y^(n+0.5)#

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)#