EXPONENTES RACIONALES: presentación (grado 11)

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EXPONENTES RACIONALES

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EXPONENTES RACIONALES

Para cualquier exponente racional m/n en sus términos más elementales, donde m y n son enteros y n > 0, definimos

a^{\frac{m}{n}}=\left(^n\sqrt{a}\right)^m\ \Longleftrightarrow\ a^{\frac{m}{n}}=\ ^n\sqrt{a^m}

Si n es par, entonces requerimos que

a\ge0

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EJEMPLO 1:

Simplifique la expresión y elimine cualquier exponente negativo

\left(4b\right)^{\frac{1}{2}}\left(8b^{\frac{1}{4}}\right)

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EJEMPLO 2:

Simplifique la expresión y elimine cualquier exponente negativo

\left(8y^3\right)^{-\frac{2}{3}}

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EJEMPLO 4:

Simplifique la expresión y elimine cualquier exponente negativo

\left(\frac{x^8y^{-4}}{16y^{\frac{4}{3}}}\right)^{-\frac{1}{4}}

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EJEMPLO 5:

Simplifique la expresión y elimine cualquier exponente negativo

\left(\frac{a^{\frac{1}{6}}b^{-3}}{x^{-1}y}\right)^3\ \left(\frac{x^{-2}b^{-1}}{a^{\frac{3}{2}}y^{\frac{1}{3}}}\right)

EXPONENTES RACIONALES

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