Indices | Commonly Made Mistakes

Humans are imperfect. Therefore to make errors in maths computation, we are reminded that we are human!

Does that mean we can excuse ourselves for making maths errors?
No...... There are maths basics that we cannot afford to make errors.

Therefore to avoid making errors in Indices, read the explanation below.
Who knows, by reading this post, you may end up one day as a professor!

Therefore to cut short everything, here it goes ......

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The format for indices are one of the simplest in maths. In its simplest form a^x = Y.

But mistakes are still being made! Why?

Firstly, 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.

Secondly, 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).

Thirdly, 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. Maths is a flexible and though-provoking subject that embodies many thinking skills. So Work hard and Enjoy Maths!

:-)

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