Can you solve this high school math quiz problem?

In this math tutorial we solve the exponential equation 11·16^(1/(x-1)) = 16^(x/(x-1)) -10 using a single elegant observation that collapses the entire equation instantly. The key insight is recognising that x/(x-1) = 1+1/(x-1), which means 16^(x/(x-1)) = 16·16^(1/(x-1)). This splits the right hand side into a clean expression involving only 16^(1/(x-1)), and the entire equation reduces to a simple linear equation in 16^(1/(x-1)). The whole problem dissolves the moment you write x/(x-1) as 1+1/(x-1). That one algebraic observation is the difference between a straightforward solution and a very long struggle. What you will learn: Why x/(x-1) = 1+1/(x-1) is the key observation that unlocks the equation How splitting 16^(x/(x-1)) into 16·16^(1/(x-1)) simplifies the right hand side How the equation reduces to a linear equation in 16^(1/(x-1)) How to verify all solutions and apply domain restrictions correctly This type of exponent splitting observation appears in math olympiad competitions, IB Mathematics Higher Level, A-Level Further Mathematics, college entrance examinations, and advanced high school algebra courses. Recognising when and how to split a fractional exponent is one of the most powerful instincts in competitive mathematics. If you found this helpful, give it a thumbs up, share it with a fellow math lover, and subscribe for weekly videos on algebra, calculus, number theory, and olympiad problem solving. Hit the notification bell so you never miss an upload. Don’t forget to like 👍, subscribe    / @nonsomaths  , and hit the notification bell for more math tips and tricks! #maths #algebra #matholympiad #mathtutorial #exponents