how do i do a2/3b3 times asquaredb1/2 divided by a3/2b1/4

[ a² / 3 · b³ ] x [ a² · b^1/2 ] / [ a^3/2 · 2b^1/4 ]

When multiplying similiar terms, add the exponent; when dividing similar terms, subtract the exponents.

For the a's:  a² x a² / a^3/2  =  a^{[ 2 + 2 - 3/2 ]}  =  a^5/2

For the b's:  b^1/2 / b³ / b^1/4   =  b^{[ 1/2 - 3 - 1/4 ]}  =  b^-11/4  =  1/b^11/4

Multiplying the numbers;  3 x 2  =  6 (in the denominator)

Answer:  a^5/2 / [ 6 · b^11/4 ]