Divide Complicated Algebraic Terms with Powers

This activity is about the division of algebraic terms with powers.

 

Example

 Simplify:

 

10a2b5

15a3b2

 

 

Answer

Remember what 10a²b⁵ and 15a³b² mean and divide them by subtracting the relevant indices.

 

We get:    

 

10 x a x a x b x b x b x b x b

15 x a x a x a x b x b

 

Cancel down a matching number of a terms from the top of the fraction with a terms from the bottom.  Similarly with b terms.

 

This leaves us with:

 

10 x b x b x b

15 x a

 

which reduces by dividing top and bottom by 5 to

 

2b3

3a

 

 

However, we need not write out our method like this each time.

 

Remember the rules of indices for division:

a^m ÷ aⁿ = a^m-n

 

In the example above, we had b⁵ ÷ b² = b^{5 - 2} = b³.

 

Let's try some questions now.