√x^5/√x^2 change to exponential notation, then simplify. assume it is positive.
sqrt ( x ^ 5 ) = ( x ^ 5 ) ^ ( 1 / 2 ) = x ^ ( 5 / 2 )
sqrt ( x ^ 2 ) = x = x ^ 1 = x ^ ( 2 / 2 )
1 / sqrt ( x ^ 2 ) = x ^ ( - 2 / 2 )
sqrt ( x ^ 5 ) / sqrt ( x ^ 2 ) =
sqrt ( x ^ 5 ) * 1 / sqrt ( x ^ 2 )
x ^ a * x ^ b = x ^ ( a + b )
x ^ ( 5 / 2 ) * x ^ ( - 2 / 2 ) =
x ^ [ 5 / 2 + ( - 2 / 2 ) ] =
x ^ ( 5 / 2 - 2 / 2 ) =
x ^ ( 3 / 2 ) =
sqrt ( x ^ 3 )