https://file.aiquickdraw.com/mathbot/file/1726686013847witrrv2r.jpg

The expression in the image is:

\[
10^{999} \cdot 5^{-999} \cdot 2^{-999}
\]

We can simplify it step by step. First, rewrite the terms involving exponents:

\[
10^{999} = (2 \cdot 5)^{999} = 2^{999} \cdot 5^{999}
\]

Thus, the expression becomes:

\[
(2^{999} \cdot 5^{999}) \cdot 5^{-999} \cdot 2^{-999}
\]

Now, simplify by canceling out the terms:

- \(5^{999} \cdot 5^{-999} = 1\)
- \(2^{999} \cdot 2^{-999} = 1\)

Therefore, the entire expression simplifies to:

\[
1
\]

So, the value of the given expression is \(1\).

Would you like further details or have any questions? Here are some related questions to expand your understanding:

1. What are the laws of exponents used to simplify such expressions?
2. How can we handle similar expressions with different bases?
3. What is the significance of negative exponents in simplifying terms?
4. How does the distributive property of exponents work in larger expressions?
5. Can you explain how the result would change if one of the exponents were slightly different?

**Tip:** When simplifying expressions with powers, always check if you can combine or cancel terms with the same base to reduce the complexity.

Simplify the expression: 10^{999} · 5^{-999} · 2^{-999}.

Learn how to simplify the exponential expression 10^999 · 5^-999 · 2^-999 step by step. This problem uses the laws of exponents to break down and simplify the terms. Suitable for students in Grades 9-11.

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