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Verified Answer :

The multiplicative inverse of a quantity - \(x\), say - denoted by \(x^{*}\), must satisfy the following:

\(xx^{*} = 1\),

giving

\(x^{*} = \frac{1}{x}\).

So in this case that \(x = \frac{4}{3a}\),

\(x^{*} = \frac{1}{(\frac{4}{3a})} = \frac{3a}{4}\)