Provide the IUPAC names for the following compounds: (I) CH3CH(Br)CH2COOH (II) CH3CH2CH(CH3)COOH

The compound contains a carboxyl group $(-\text{COOH})$, so it is a carboxylic acid. The carbon of the carboxyl group is C1.

Numbering starts from the carboxyl carbon (C1).
The main chain is: $\text{CH}_3\text{CH}(\text{Br})\text{CH}_2-\text{COOH}$.
This chain has 4 carbons, making the parent acid butanoic acid.

There is a bromine atom $(\text{Br})$ on C3.

The name is 3-bromobutanoic acid.

The name of compound (I) is: $\boxed{\text{3-bromobutanoic acid}}$

II)

The compound contains a carboxyl group $(-\text{COOH})$, so it is a carboxylic acid. The carbon of the carboxyl group is C1.

Numbering starts from the carboxyl carbon (C1).
The main chain is: $\text{CH}_3\text{CH}_2\text{CH}(\text{CH}_3)-\text{COOH}$.
This chain has 4 carbons, making the parent acid butanoic acid.

There is a methyl group $(\text{CH}_3)$ on C2.

The name is 2-methylbutanoic acid.

The name of compound (II) is: $\boxed{\text{2-methylbutanoic acid}}$

III)

The compound contains a carboxyl group $(-\text{COOH})$, so it is a carboxylic acid. The carbon of the carboxyl group is C1.

Numbering starts from the carboxyl carbon (C1).
The structure is:

The longest continuous carbon chain that includes the carboxyl carbon (C1) is 5 carbons long:
$\text{C1}(\text{COOH})-\text{C2}(\text{CH})-\text{C3}(\text{CH}_2)-\text{C4}(\text{CH})-\text{C5}(\text{CH}_3)$.
This makes the parent acid pentanoic acid.

There is a propyl group $(\text{CH}_2\text{CH}_2\text{CH}_3)$ on C2.
There is a methyl group $(\text{CH}_3)$ on C4.

The name is 4-methyl-2-propylpentanoic acid.

The name of compound (III) is: $\boxed{\text{4-methyl-2-propylpentanoic acid}}$