Take a simple example

2^3 - 2^2 = 4

Take 2^2 thats common

2^2 (2 - 1) = 4

Exponent rule: a^b*a^c = a^(b+c)

In the example from 5^13-5^12 , 5^12 has been taken out as a common factor

5^12 ( 5 - 1)

5^12 (5^1 - 5^0) (5 is 5^1 and 1 can euqal 5^0 i.e Any number to the exponent 0 is 1)

Expand this using a^b*a^c = a^(b+c)

= 5^12*5^1 (a=5 b=12 c=1) - 5^12*5^0 (a=5 b=12 c=0)

= 5^(12+1) - 5^(12+0)

= 5^13-5^12

Hope this helps!


Regards,
CR

5^12 - 6(5^13 - 5^12)
= 5^12-6(5*5^12 - 5^12) Splitting the power to make a common term
= 5^12 - 6*5^12(5-1) Taking common out.

Thanks guys. I appreciate the response.