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:
$sqrt(x) = x^(1/2)$

$sqrt(x) ^(2n) = (x^(1/2))^(2n)$
$(x^(1/2))^(2n) = x^(1n) = x^n$

$sqrt(y) ^(2n+1) = (y^(1/2))^(2n+1)$
$(y^(1/2))^(2n+1) = y^(n+0.5)$

$y^(n+0.5) = y^n * y^0.5 = sqrty *y^n$

$sqrtx^(2n)⋅sqrty^(2n+1) = x^n * sqrty *y^n$

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

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