The expression you've written is a bit complex, but I will attempt to break it down step by step for clarity.

Let's rewrite it with parentheses to avoid ambiguity:

$2^{10} \times 3^{10} - 2^{10} \times 3^9 / 2^9 \times 3^{10}$

To simplify this, I will follow the standard order of operations (PEMDAS):

1. Exponents: First, we evaluate all powers (exponents).
2. Multiplications and Divisions: Then we perform the multiplication and division from left to right.
3. Subtraction: Lastly, perform the subtraction.

Let’s go ahead and simplify this step-by-step.

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Step 1: Evaluate the powers:

$2^{10} = 1024, \quad 3^{10} = 59049, \quad 3^9 = 19683, \quad 2^9 = 512$

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Step 2: Plugging these into the expression:

$1024 \times 59049 - \frac{1024 \times 19683}{512 \times 59049}$

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Step 3: Simplify the multiplication and division:

First, compute the multiplication in both terms:

$1024 \times 59049 = 60466176$

For the second term, let's handle the division and multiplication:

$\frac{1024 \times 19683}{512 \times 59049} = \frac{201326592}{30233088} = 6.6667$

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Step 4: Subtract:

$60466176 - 6.6667 \approx 60466169.3333$

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Thus, the result of the given expression is approximately:

$60466169.3333$

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Would you like to go into further detail on how the powers were simplified, or explore anything else related to this problem?

Here are some follow-up questions that could help expand on this:

1. How does the order of operations affect the way we approach such expressions?
2. What would happen if you had used fractions instead of exponents in this expression?
3. How can logarithms be used to simplify expressions with large exponents?
4. Can we apply any factoring techniques to simplify such a problem before solving it?
5. How do exponential functions grow when their bases are greater than 1?

Tip: When dealing with large exponents, consider breaking the problem into smaller components (like evaluating powers separately) and simplify before multiplying or dividing.