contestada

Which expressions are equivalent to z^{0.2}z 0.2 z, start superscript, 0, point, 2, end superscript ? Choose all answers that apply: Choose all answers that apply: (Choice A) A \sqrt[5]{z} 5 z ​ root, start index, 5, end index (Choice B) B \sqrt{z} z ​ square root of, z, end square root (Choice C) C \left(z^2\right)^{-10}(z 2 ) −10 left parenthesis, z, squared, right parenthesis, start superscript, minus, 10, end superscript (Choice D) D None of the above

Respuesta :

Answer:

[tex]z^{\frac{1}{5} } and \sqrt[5]{z}[/tex]

Step-by-step explanation:

Given the expression [tex]z^{0.2}[/tex], the following is equivalent to the expression;

First we convert the decimal to a fraction

[tex]z^{0.2}\\= z^{\frac{2}{10} }\\\= z^{\frac{1}{5} }[/tex]

According to one of the laws of indices;

[tex]a^{\frac{m}{n} }= \sqrt[n]{m}[/tex]

Applying this to the resulting indices above;

[tex]z^{\frac{1}{5} } = (\sqrt[5]{z})^{1} \\= \sqrt[5]{z}[/tex]

Based on the calculation above, the expressions that is equivalent to [tex]z^{0.2}[/tex] are [tex]z^{\frac{1}{5} } and \sqrt[5]{z}[/tex]

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