Hi Lindy
These took some tracking down!
I hadn't come across the place "Tydee" before but google told me it was near or in Rogerstone. I thought it odd that almost all the members of the family had the same birthplace, when spread over so many years so I looked at the enumerators image for 1881. It has been mistranscribed. The last person in the household above them was born in "Monmouth, Tydee". The first person in the Powell Household was born in "Glamorgan" and the others were all dittoed down until it came to the nieces. So basically instead of birthplace "Tydee", they should all read "Glamorgan".
So Glamorgan was not a lot of help, however knowing that they were in Cardiff in 1881 and with a bit of jumping from 1871 to 1861 and back it does seem that Edward and his brother William were born in Neath. Here is what I have found:
1861 - 9 Eleanor Street, Cardif St Mary
Edward Powell, Head, Married, 25, Boilermaker born Neath Abbey
Elizabeth Powell, Wife, Married, born 21, Cowbridge
George Powell, Son, 3 months, born Cardiff
Jno Williams, Cousin, Single, 31, born Neath Bryncoch
In 1871: 21 Comet Street, Roath, Cardiff
Edward Powel, Head, Married, 34, Boilermaker, born Neath
Elizabeth Powel, Wife, 30, born Cowbridge
George Powel, Son, 11, Scholar, born Cardiff
Elizabeth Powel, Daughter, 7, born Cardiff
Annie Powel, Daughter, 4, born Cardiff
Edward Powel, Son, 2, born Cardiff
I also found a William Powell, aged 33, an Engine Fitter, born Neath lodging at Maria Street, Cardiff St Mary. The age doesn't quite match with Edward's brother William in 1881 but the occupationsof Engine fitter does match with 1881. As does the occupation of Boilermaker for Edward Powell in the 1861, 1871 and 1881,
Hope this helps
Caro
Census Transcriptions - Crown Copyright, National Archives