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The elementary symmetric functions play a crucial role in the study of zeros of non-zero polynomials in <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="double-struck">C</mi> <mo>[</mo> <mi>x</mi> <mo>]</mo> </mrow> </semantics> </math> </inline-formula>, and the problem of finding zeros in <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="double-struck">Q</mi> <mo>[</mo> <mi>x</mi> <mo>]</mo> </mrow> </semantics> </math> </inline-formula> leads to the definition of algebraic and transcendental numbers. Recently, Marques studied the set of algebraic numbers in the form <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <msup> <mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> </semantics> </math> </inline-formula>. In this paper, we generalize this result by showing the existence of algebraic numbers which can be written in the form <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>P</mi> <mn>1</mn> </msub> <msup> <mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </msup> <mo>⋯</mo> <msub> <mi>P</mi> <mi>n</mi> </msub> <msup> <mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>Q</mi> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </msup> </mrow> </semantics> </math> </inline-formula> for some transcendental number <i>T</i>, where <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>&#8230;</mo> <mo>,</mo> <msub> <mi>P</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>&#8230;</mo> <mo>,</mo> <msub> <mi>Q</mi> <mi>n</mi> </msub> </mrow> </semantics> </math> </inline-formula> are prescribed, non-constant polynomials in <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="double-struck">Q</mi> <mo>[</mo> <mi>x</mi> <mo>]</mo> </mrow> </semantics> </math> </inline-formula> (under weak conditions). More generally, our result generalizes results on the arithmetic nature of <inline-formula> <math display="inline"> <semantics> <msup> <mi>z</mi> <mi>w</mi> </msup> </semantics> </math> </inline-formula> when <i>z</i> and <i>w</i> are transcendental.