Grades 11-12 Video Solutions 2021-video 2021 11-12/7

Video Transcription

Video Summary

The problem involves comparing powers and roots of a number \( x = \frac{\pi}{4} \), which is less than 1. When numbers less than 1 are raised to higher powers, the results get smaller: \( x^4 < x^2 < x \). Conversely, taking roots results in larger numbers: \( \sqrt[4]{x} > \sqrt{x} > x \). Therefore, among the different expressions of \( x \), the fourth root is the largest. Thus, the largest value given the options is the fourth root of \( x \), corresponding to option "e."

Keywords

powers

roots

comparison

fourth root

largest value