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Answer :

Answer:

D

Step-by-step explanation:

Given expression :

  • [tex]\sqrt[4]{x^{2}y^{3}z }[/tex]

Solving :

  • A number with the 4th root is the same as a number raised to the power 1/4
  • [tex](x^{2})^{1/4}(y^{3})^{1/4}(z)^{1/4}[/tex]
  • [tex]x^{\frac{1}{2}} y^{\frac{3}{4}}z^{\frac{1}{4} }[/tex] [Option D]
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Answer:

D   [tex]\sf x^{\frac12} y^{\frac34} z^{\frac14}[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{\sf x^2y^3z}=\sqrt[4]{\sf x^2y^3z^1}[/tex]

Apply the Radical Product Rule  [tex]\sqrt{\sf ab} =\sqrt{\sf a}\sqrt{\sf b}[/tex] :

[tex]\implies \sqrt[4]{\sf x^2}\sqrt[4]{\sf y^3}\sqrt[4]{\sf z}[/tex]

Apply fractional exponent rule [tex]\sqrt[n]{\sf a^m} = \sf a^{\frac{m}{n}}[/tex] :

[tex]\sf \implies x^{\frac24} y^{\frac34} z^{\frac14}[/tex]

Simplify:

[tex]\sf \implies x^{\frac12} y^{\frac34} z^{\frac14}[/tex]

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