To simplify the expression
(3a0.5)(512�30�−76)1/4(3a0.5)(512a30b−76)1/4,
let's first deal with the terms inside the parentheses.
512�30�−76512a30b−76 can be broken down into 512�30512a
Now, apply the rules of exponents:
(512�30�−76)1/4=(5121/4�30⋅14�−76⋅14)(512a30b−76)1/4=(5121/4a30⋅41