10000000000000000000000000000000000090000000000000999999* 10000000000000000000000000000000000090000000000000999999

To multiply the two large numbers:

\[ (10^{36} + 9 \times 10^{33}) \times (10^{36} + 9 \times 10^{33}) \]

Let \( x = 10^{36} \) and \( y = 9 \times 10^{33} \). Thus, we can rewrite the expression as:

\[ (x + y) \times (x + y) = x^2 + 2xy + y^2 \]

Now, we calculate each component:

1. \( x^2 = (10^{36})^2 = 10^{72} \)
2. \( 2xy = 2 \times 10^{36} \times 9 \times 10^{33} = 18 \times 10^{69} \)
3. \( y^2 = (9 \times 10^{33})^2 = 81 \times 10^{66} \)

Now putting it all together:

\[ 10^{72} + 18 \times 10^{69} + 81 \times 10^{66} \]

We can express this in a cleaner form, factoring out the largest power of ten:

\[ 10^{66} (10^6 + 18 \times 10^3 + 81) \]

Now we calculate the expression in the parentheses:

\[ 10^6 = 1000000, \quad 18 \times 10^3 = 18000, \quad 81 = 81 \]

Adding these together:

\[ 1000000 + 18000 + 81 = 1018081 \]

Thus, the final result can be expressed as:

\[ 10^{66} \times 1018081 \]

In full numerical form, that is:

\[ 1018081000000000000000000000000000000000000 \]

So the product of the two numbers is:

\[ \boxed{1018081000000000000000000000000000000000000} \]