What is the IUPAC name of (CH_3)_2CH-COOH ?

The given compound is $(\text{CH}_3)_2\text{CH-COOH}$.

The longest carbon chain containing the principal functional group ($-COOH$) has $3$ carbon atoms.

Numbering starts from the carboxyl carbon:
C-1: $-COOH$
C-2: $-CH(CH_3)-$
C-3: $-CH_3$

There is a methyl substituent at the second carbon atom.

Therefore, the IUPAC name of the compound is 2-Methylpropanoic acid.

Answer: 2-Methylpropanoic acid