Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Given the expression $z^{0.2}$, the following is equivalent to the expression;

First we convert the decimal to a fraction

$z^{0.2}\\= z^{\frac{2}{10} }\\\= z^{\frac{1}{5} }$

According to one of the laws of indices;

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

Applying this to the resulting indices above;

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

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