
First, we can simplify each expression:
(10⁰x10¹x1¹⁰) = 10¹¹
(10x10¹) = 100
(10⁰+10¹+1¹⁰) = 1 + 10 + 1,000,000,000 = 1,000,000,011
(10⁰+10¹x1¹⁰) = 10¹⁰
Now we can arrange them in increasing order:
10¹¹ < 10¹⁰ < 100 < 1,000,000,011
So the correct order from smallest to largest is:
(10⁰x10¹x1¹⁰) (10⁰+10¹x1¹⁰) (10 x 10¹) (10⁰+10¹+1¹⁰)
or
(10¹¹) (10¹⁰) (100) (1,000,000,011)