To simplify the expression \( 1785 \times 1789 \) in terms of exponents, we can use the identity for the product of two numbers that are evenly spaced around a midpoint.
We can rewrite the numbers as follows:
\[ 1785 = 1787 - 2 \] \[ 1789 = 1787 + 2 \]
Thus, we can express the product as:
\[ (1787 - 2)(1787 + 2) \]
This is a difference of squares, which can be simplified using the formula \( (a - b)(a + b) = a^2 - b^2 \).
Letting \( a = 1787 \) and \( b = 2 \), we have:
\[ (1787 - 2)(1787 + 2) = 1787^2 - 2^2 \]
Now we calculate \( 2^2 \):
\[ 2^2 = 4 \]
Therefore, the expression simplifies to:
\[ 1787^2 - 4 \]
This can't be simplified further without calculating \( 1787^2 \). The final answer expressed as a single term using exponents is:
\[ 1787^2 - 4 \]