Question

simplify each radical expression as much as possible. assume that the variables represent any real numbers. use the absolute value button only when necessary. (a) \\(\sqrt4{z^4} = \square\\) (b) \\(\sqrt6{(5 - 5w)^6} = \square\\)

Explanation:

Step1: Simplify even root of $z^4$

Recall $\sqrt[n]{x^n}=|x|$ for even $n$. Here $n=4$, so $\sqrt[4]{z^4}=|z|$.

Step2: Simplify even root of $(5-5w)^6$

For $n=6$ (even), $\sqrt[6]{(5-5w)^6}=|5-5w|$, which factors to $5|1-w|$ or $|5-5w|$.

Answer:

(a) $|z|$
(b) $|5-5w|$ (or equivalent $5|1-w|$)