First, we need to understand the properties of exponents. When we divide like bases, we subtract the exponents. This means what we are doing here essentially is equivalent to calculating y^n1 / y^n2 = y^(n1-n2), where n1 = 1/10 and n2 = 1/20.
We perform the subtraction of the exponents which is 1/10 (n1) - 1/20 (n2). The result is 0.05.
But the given expression is (y^((1)/(10)))/(y^((1)/(20))) multiplied by y^((1)/(10)).
In multiplication, we add the exponents when the bases are the same. So, we add y^n3 to the result we found above, where n3 = 1/10.
0.05 + 1/10 equates to 0.15.
So, the simplified expression is y^(0.05) * y^(0.15), which can be simplified further to y^0.2, by applying the rules of exponents again.