Question

simplify the expression. $sqrt4{\frac{k^{16}}{16z^{4}}} = \frac{square}{square}$

Explanation:

Step1: Split root into numerator/denominator

$$\sqrt[4]{\frac{k^{16}}{16z^4}} = \frac{\sqrt[4]{k^{16}}}{\sqrt[4]{16z^4}}$$

Step2: Simplify numerator root

$$\sqrt[4]{k^{16}} = k^{\frac{16}{4}} = k^4$$

Step3: Simplify denominator root

$$\sqrt[4]{16z^4} = \sqrt[4]{16} \cdot \sqrt[4]{z^4} = 2|z|$$
(Note: For even roots, we use absolute value to ensure non-negativity; if $z$ is assumed positive, this can be written as $2z$.)

Answer:

$\frac{k^4}{2|z|}$ (or $\frac{k^4}{2z}$ if $z>0$)