To simplify the expression, let's start by evaluating the exponents:

(2/3)^9 = (2^9)/(3^9) = 512/19683
(2/3)^7 = (2^7)/(3^7) = 128/2187

Now, substitute these values back into the expression:

-1/2 - (512/19683) : (128/2187) + 5/6

Next, let's simplify the division:

-1/2 - (512/19683) * (2187/128) + 5/6

Now, let's simplify the multiplication:

-1/2 - (512 * 2187) / (19683 * 128) + 5/6

Next, let's simplify the division:

-1/2 - 1119744 / 2519424 + 5/6

Now, let's find a common denominator for the fractions:

-1/2 - (1119744 * 3) / (2519424 * 3) + (5 * 2) / (6 * 2)

Simplifying the multiplication:

-1/2 - 3359232 / 7558272 + 10 / 12

Now, let's find a common denominator for the fractions:

-1/2 - (3359232 + 10 * 629856) / (7558272 * 6)

Simplifying the multiplication:

-1/2 - (3359232 + 6298560) / 45349632

Now, let's simplify the addition:

-1/2 - 9657792 / 45349632

Now, let's find a common denominator for the fractions:

-1/2 - (9657792 * 2) / (45349632 * 2)

Simplifying the multiplication:

-1/2 - 19315584 / 90699264

Now, let's simplify the subtraction:

(-1 - 19315584) / 90699264

Finally, let's simplify the numerator:

-19315585 / 90699264

Therefore, the simplified expression is -19315585/90699264.