B737 TAXIING FOR DEP AT PBI CROSSED RWY WITHOUT CLRNC.

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WE ARRIVED PBI AFTER OUR SCHEDULED DEP TIME DUE TO LATE DEP FROM PHL AND WX DEV IN THE PBI AREA. WE PUSHED BACK 35 MINS LATE OUT OF GATE. WHEN THE FO CALLED FOR TAXI; WE WERE CLRED TO TAXI TO RWY 27R. HE READ BACK '27R' AND I REPEATED '27R;' HOWEVER; MY BRAIN HEARD '9L' (READBACK/HEARBACK). AS I BEGAN TO TAXI; THE FO WAS HEADS DOWN GETTING WT AND BAL INFO FROM ACARS AS HE WAS NOT EXPECTING A RWY XING AND IT'S ONLY A SHORT DISTANCE FROM GATE TO RWY 13/31. AS I STARTED ACROSS RWY 13/31; AFTER CHKING FOR TFC; I REALIZED MY MISTAKE AND SHORTLY THEREAFTER GND CTL QUESTIONED US. ALTHOUGH WE WERE NOT RUSHING; WE WERE STRESSED AND RWY 9L IS THE RWY IN USE AT PBI MOST OF THE TIME. IN THE FUTURE; I WILL HAVE MY FO'S MONITOR MY TAXI RTE UNTIL THEY SEE THAT I HAVE STARTED OFF THE CORRECT WAY; BEFORE GOING HEADS DOWN. SUPPLEMENTAL INFO FROM ACN 615875: I WENT HEADS DOWN IN THE COCKPIT AND STARTED CHKING AND LOADING THE WT AND BAL DATA IN THE COMPUTER. MY FIRST INDICATION WE TURNED IN THE WRONG DIRECTION WAS WHEN GND ASKED US WHERE WE WERE GOING.