Common Mistakes

In indices, we can write the simplest form as a^x = Y.

But mistakes are still being made! Why?

First, the writing skill of students has to improve.
When the power of a number (base) has to be written higher up and smaller than the base number, it has to be so.
Error: a^x = Y written as ax = Y ==> the power "x" has changed meaning.

Second, understanding of the Laws of Indices is not fully digested.
Error: a⁰ = 1 misunderstood as a⁰ = 0 ==> concept of power is wrong as it became multiplication instead of division (e.g. a² / a² = 1).

Third, the function of brackets is not fully used.
Brackets can isolate the powers when many manipulations or operations are done to simplify index terms.
Error-1: x⁴ / x ^2-n = x^4-(2-n) = x²⁺ⁿ became = x^4-2-n = x^2-n . The sign for the small "n" is wrong.

Error-2: (xK)² = x² K² taken as x K² forgetting that "x" is affected by the power 2 also.

How to solve this common indices mistakes?
Practice and practice, and clarify thoughts. This is different from learning other subjects where practicing of questions are not that intensive. 

Below is one example video of correcting common mistakes that students always do in fractional indices. After watch this video we hope there's no more confusing in answering similar questions!

Example:

"Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere."

by W. S. Anglin