Exponents, it's all Greek to me!

[Ivy guy]

I have been revising my exponents lately. I need someone to help me with this:

2^20 - 2^19 = 2^19

I have memorised this rule but how does one arrive at such as answer? Can someone explain the steps to the final answer? Comments welcome.

Cheers...

[Ankost]

2^20-2^19=2^19*2-2^19=2^19(2-1)= 2^19
Exponents are the product of the base (in this case base=2) n times (n in this case=20). 2*2*2*..... So 2^20 we can express as 2^19*2.

[Lodestar]

Please find below a simple expln.,

(2^20-2^19) = (2^19)

we can write the above expression as:

-> ((2^19)*2-2^19)
-> 2^19*(2-1) (taking 2^19 common)
-> 2^19

Hence proved.

[miaw99]

qn: 2^20 - 2^19 = 2^19

x= a^19

y= a^20 = 2 * 2^19
y= 2x

then:
2x - x = x

so the result is x = a^19