Calculation of the value of the given expression:
• Let's break down the given expression step by step:

Step 1: Calculate 1/(1 + 8) = 1/9 = 1/9

Step 2: Calculate (1 + 8)^Y = 9^Y

Step 3: Calculate (1/(1 + 8))^X = (1/9)^X = 1/9^X

Step 4: Substitute the values back into the expression:
(1/9)^Y - 1/9^X

Step 5: Simplify the expression further if required based on the values of X and Y.

Explanation:
• The given expression involves exponentiation and fractions. By breaking down the expression into smaller parts and simplifying each part individually, we can calculate the overall value of the expression. It is important to follow the order of operations (PEMDAS) to ensure the correct calculation of the expression.
• The expression can be simplified using basic exponent rules and fraction operations. By substituting the calculated values back into the expression, we can arrive at the final value.
• It is crucial to pay attention to the signs and terms in the expression to avoid errors in calculation. Taking each step carefully and double-checking the calculations can help in accurately determining the value of the given expression.
Overall, by following the steps mentioned above and applying fundamental mathematical principles, we can determine the value of the given expression effectively.