My sister is old enough to go to aerobics class by herself.

Literal

Younger-sister [topic-は] alone aerobics-class [to-に] can-go age.

一人で ('by oneself') + 行ける (potential form of 行く) = 'can go alone.' 年齢だ ('is the age for') uses the copula to state she's at the right age. エアロビクスクラス is a katakana loanword compound.