Laws of Indices

This item is taken from IGCSE Mathematics (0580) Paper 21 of October/November 2009.

To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Algebra
   (b) Specific topic: Indices
   (c) Formula Needed:

First, let us rewrite the given expressions:

Now the expression is of the form a/b. Next step is

We can still simplify the exponent and the coefficient:

Therefore,

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