Respuesta :

MsRay

Answer:

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

Step-by-step explanation:

According to the laws of exponents, when exponents with the same base are divided, you keep the base and subtract the exponents:

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

[tex]y^{\frac{-1}{3}-\frac{1}{2}}=y^{\frac{-2}{6}-\frac{3}{6}}=y^{\frac{-5}{6}}[/tex]

Also according to the laws of exponents, when the exponent is negative, you put the base under '1' (turn it into a fraction) and make the exponent positive:

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

MrRoyal

A simplified expression involves rewriting an expression in a simpler form

The simplified expression of [tex]\frac{x^{1/2} y^{-1/3}}{x^{1/4}y^{1/2}}[/tex] is [tex]\frac{x^{1/2}}{ y^{5/6}}[/tex]

The expression is given as:

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

Apply the rule of indices

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

Evaluate the exponents (i.e. add and subtract)

[tex]x^{1/2} y^{-5/6}[/tex]

Apply the rule of indices, again

[tex]\frac{x^{1/2}}{ y^{5/6}}[/tex]

Hence, the simplified expression of [tex]\frac{x^{1/2} y^{-1/3}}{x^{1/4}y^{1/2}}[/tex] is [tex]\frac{x^{1/2}}{ y^{5/6}}[/tex]

Read more about expressions at:

https://brainly.com/question/723406

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