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India
Class IX

Division law with integer or variable bases and integer negative powers

Lesson

We've already learnt about the division rule which states:

$a^x\div a^y=a^{x-y}$ax÷​ay=axy

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.

Remember!
  • Subtracting a negative term is the same as adding a positive term, e.g. $2-\left(-5\right)=2+5$2(5)=2+5$=$=$7$7

  • Adding a negative term is the same as subtracting the term, e.g. $6+\left(-10\right)=6-10$6+(10)=610$=$=$-4$4

 

Since we are working with directed numbers, it is important the we're also familiar with the negative index law, which states $a^{-x}=\frac{1}{a^x}$ax=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}\div10^4$1010÷​104 in the form $a^n$an.


Question 2

Simplify the following, giving your answer with positive indices: $\frac{5p^5q^{-4}}{40p^5q^6}$5p5q440p5q6

Question 3

Rewrite the following expression using positive index notation with a single base: $\frac{1}{9\times9\times9\times9}\times\frac{1}{9\times9}$19×9×9×9×19×9.

 

Outcomes

9.NS.RN.3

Recall of laws of exponents with integral powers. Rational exponents with positive real bases

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