If \( \sqrt[4]{x^3} \cdot \sqrt[3]{x^2} = x^a \) for all values of \(x\), what is the value of \(a\)?

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Simplification is easier when the exponents are written in fractional form:

$$ \sqrt[4]{x^3} \cdot \sqrt[3]{x^2} = x^{\frac{3}{4}} \cdot x^{\frac{2}{3}}$$ $$ = x^{\frac{3}{4}+\frac{2}{3}} $$ $$ = x^{\frac{9}{12}+\frac{8}{12}} $$ $$ = x^{\frac{17}{12}} $$