Division law with integer or variable bases and integer negative powers
We've already learnt about the division rule which states:
$$ax÷ay=ax−y
What happens when we encounter questions that include negative indices? The same rule applies. We just need to remember the rule for working with negative numbers.
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Subtracting a negative term is the same as adding a positive term, e.g. $$2−(−5)=2+5$$=$$7
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Adding a negative term is the same as subtracting the term, e.g. $$6+(−10)=6−10$$=$$−4
Since we are working with directed numbers, it is important the we're also familiar with the negative index law, which states $$a−x=1ax, just in case we're asked to express a negative index and a positive index or vice versa.
Examples
Question 1
Rewrite $$10−10÷104 in the form $$an.
Question 2
Simplify the following, giving your answer with positive indices: $$5p5q−440p5q6
Question 3
Rewrite the following expression using positive index notation with a single base: $$19×9×9×9×19×9.