Respuesta :

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ [/tex]

[tex]\bf \cfrac{x^{\frac{1}{2}}y^{-\frac{1}{3}}}{x^{\frac{1}{4}}y^{\frac{1}{2}}}\implies \cfrac{x^{\frac{1}{2}}x^{-\frac{1}{4}}}{y^{\frac{1}{2}}y^{\frac{1}{3}}}\implies \cfrac{x^{\frac{1}{2}-\frac{1}{4}}}{y^{\frac{1}{2}+\frac{1}{3}}}\implies \cfrac{x^{\frac{2-1}{4}}}{y^{\frac{3+2}{6}}}\implies \cfrac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]
boffeemadrid

Answer:

(A)[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]

Step-by-step explanation:

The given expression is:

[tex]\frac{x^{\frac{1}{2}}y^{\frac{-1}{3}}}{x^{\frac{1}{4}}y^{\frac{1}{2}}}[/tex]

Upon solving the given expression, we get

=[tex]{x^{\frac{1}{2}-\frac{1}{4}}{\cdot}}{y^{\frac{-1}{3}-\frac{1}{2}}}[/tex] (using the property of exponents and powers that if base is same then the powers gets added.)

=[tex]x^{\frac{1}{4}}{\cdot}y^{\frac{-5}{6}}[/tex]

=[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]

which is the required simplified form of the given equation.

Hence, option A is correct.

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