How would you explain to your friend why the quotient of x^8 and x^2 is x^6 and not x^4 ?

Question

anonymous · Answer

Rewrite x^8 as x*x*x*x*x*x*x*x/x*x. Simplify using division to get x*x*x*x*x*x which is the same as x^6

anonymous · Answer

Whi isn't it the same as x^4?

anonymous · Answer

Because you can't treat exponents like multiplication. While 8x/2x = 4x, x^6/x^2 = x^6. Basically, (x^a)/(x^b) = x^(a-b)

anonymous · Answer

Is there a much more simple way of writing the x^8 and x^2

anonymous · Answer

$$x^8 = x*x*x*x*x*x*x*x$$ or $$x^2^3$$

amistre64 · Answer

Like terms cancel in fractions:
x^8 means you have 8 little "x"s on top part
x^2 means you have 2 little "x"s on the bottom part

cancel 2 little "x"s from the top and your left with 6 little "x"s.
cancel 2 little "x"s from the bottom and your left with the number "1".

6 little "x"s over the number "1" means x^6 :)