This math topic focuses on applying the power law of exponents, particularly in cases where the base involves roots and algebraic manipulation. It is designed for those learning about negative, fractional, and power laws of exponents. The problems involve equations where learners must solve for the variable \( x \) by equating expressions with exponential and root functions, leveraging their understanding of how to manipulate exponents algebraically to isolate and determine \( x \). This is aimed at enhancing algebraic skills in handling powers and roots systematically.