Let's simplify the given expression step by step:

The expression is:

$G = (2^{1+1}-1)^2 \cdot (8-9) = -9$

1. Simplify inside the exponents and parentheses:

   • Calculate $2^{1+1}$: $2^{1+1} = 2^2 = 4$
   • Substitute back into the expression: $(2^{1+1} - 1)^2 = (4 - 1)^2 = 3^2 = 9$

2. Simplify the second part inside the parentheses:

   • Calculate $8 - 9$: $8 - 9 = -1$

3. Multiply the results from steps 1 and 2:

   • Now, multiply: $9 \cdot (-1) = -9$

Thus,

$G = -9$

So, the given equation is correct as stated:

$(2^{1+1} - 1)^2 \cdot (8 - 9) = -9$

Would you like more details, or do you have any questions?

Here are some related questions you might find interesting:

1. How do you simplify more complex exponents within an equation?
2. What are the properties of exponents that are useful for simplification?
3. How do you solve equations with multiple operations?
4. What are some common mistakes to watch out for when simplifying expressions?
5. How can you use parentheses to structure calculations correctly?

Tip: Always perform operations inside parentheses first, followed by exponents, multiplication/division, and addition/subtraction (PEMDAS/BODMAS rules).