To find the ratio, you just need to divide the two function and solve it. The calculation would be:
<span>F(t)=Q0(1+r)^t
F(0.11)/F(0.01) = 1.09/1.06
</span>Q0(1+r)^0.11 / Q0(1+r)^0.01 = 1.0291
(1+r)^(0.11-0.01) = <span>1.0291</span>
(1+r)^0.10 = 1.0291
(1+r)^0.10*10 = 1.0283 ^10
(1+r )= 1.3325
r = 0.323
For this equation, all are subtraction symbols which means you don't need to care about the parenthesis as they do nothing.
Basically, it's the associative property because the parenthesis do nothing to the equation and both sides stay the same