Find the following. Assume that letters can represent any real number.
-$\sqrt[416]{(a+b)^{416}}$
A) $|a+b|$
B) $\sqrt[208]{(a+b)}$
C) $a+b$
D) $\sqrt{(a+b)^{208}}$

Question

Quizplus · Accepted Answer

The expression $\sqrt[416]{(a+b)^{416}}$ simplifies to $|a+b|$ because when you take an even root of an even power, the result is the absolute value of the base. This accounts for the fact that raising a negative number to an even power results in a positive number, and taking an even root of a positive number can yield a positive or negative result, hence the absolute value.

Find the Following (a+b)416416\sqrt[416]{(a+b)^{416}}416(a+b)416​ A) ∣a+b∣|a+b|∣a+b∣ B) (a+b)208\sqrt[208]{(a+b)}208(a+b)​ C) a+ba+ba+b D) (a+b)208\sqrt{(a+b)^{208}}(a+b)208​

Find the Following $\sqrt[416]{(a+b)^{416}}$ A) $|a+b|$ B) $\sqrt[208]{(a+b)}$ C) $a+b$ D) $\sqrt{(a+b)^{208}}$