To simplify and calculate the expression

\[
\left( \frac{2^2}{3} \right) \times \left( \frac{3^2}{8} \right) \times \left( \frac{4^2}{15} \right) \times \left( \frac{5^2}{24} \right) \times \left( \frac{6^2}{35} \right) \times \left( \frac{7^2}{48} \right) \times \left( \frac{8^2}{63} \right) \times \left( \frac{9^2}{80} \right)
\]

we begin by identifying the pattern in the denominator.

The denominators are as follows:

- \(3 = 1 \cdot 3\)
- \(8 = 2^3\)
- \(15 = 3 \cdot 5\)
- \(24 = 4! = 4 \cdot 6\)
- \(35 = 5 \cdot 7\)
- \(48 = 6 \cdot 8\)
- \(63 = 7 \cdot 9\)
- \(80 = 8 \cdot 10\)

Now let's denote this product as \( P \):

\[
P = \frac{2^2 \cdot 3^2 \cdot 4^2 \cdot 5^2 \cdot 6^2 \cdot 7^2 \cdot 8^2 \cdot 9^2}{3 \cdot 8 \cdot 15 \cdot 24 \cdot 35 \cdot 48 \cdot 63 \cdot 80}
\]

We first calculate the numerator:

\[
2^2 \cdot 3^2 \cdot 4^2 \cdot 5^2 \cdot 6^2 \cdot 7^2 \cdot 8^2 \cdot 9^2 = (2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8 \cdot 9)^2
\]

Now calculating \( 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8 \cdot 9 \), which is \( 9! \):

\[
9! = 362880
\]

So the numerator becomes:

\[
(9!)^2 = (362880)^2
\]

Now calculate the denominator:

1. **Compute the denominators explicitly**:
- \( 3 = 3 \)
- \( 8 = 2^3 = 8 \)
- \( 15 = 3 \cdot 5 = 15 \)
- \( 24 = 4! = 24 \)
- \( 35 = 5 \cdot 7 = 35 \)
- \( 48 = 6 \cdot 8 = 48 \)
- \( 63 = 7 \cdot 9 = 63 \)
- \( 80 = 8 \cdot 10 = 80 \)

Calculating the product of the denominators:

\[
3 \cdot 8 \cdot 15 \cdot 24 \cdot 35 \cdot 48 \cdot 63 \cdot 80
\]

Calculating step by step:

- \(3 \cdot 8 = 24\)
- \(24 \cdot 15 = 360\)
- \(360 \cdot 24 = 8640\)
- \(8640 \cdot 35 = 302400\)
- \(302400 \cdot 48 = 14515200\)
- \(14515200 \cdot 63 = 915840000\)
- \(915840000 \cdot 80 = 73267200000\)

Thus, the denominator is \( 73267200000 \).

Finally, we can compute the entire expression \( P = \frac{(9!)^2}{3 \cdot 8 \cdot 15 \cdot 24 \cdot 35 \cdot 48 \cdot 63 \cdot 80} \):

\[
P = \frac{(362880)^2}{73267200000}
\]

Calculating \( (362880)^2 = 131681894400 \).

Thus,

\[
P = \frac{131681894400}{73267200000} \approx 1.795 (approx)
\]

After final simplification, if you want an exact fraction, we would reduce

However, it ends quite close to 1.8. Thus, the final answer is:

\[
P \approx 1.8
\]
So the final boxed answer is:

\[
\boxed{1.8}
\]