To simplify the expression \((2 - 3 \cdot 9^3) - 429 \cdot 9^{-10}\), we will apply the properties of exponents.
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Simplify \(9^3\): \[ 9^3 = 729 \]
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Now substitute \(9^3\) back into the expression: \[ 2 - 3 \cdot 729 = 2 - 2187 = -2185 \]
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The expression now is: \[ -2185 - 429 \cdot 9^{-10} \] In this step, we can convert the negative exponent to a positive one: \[ 9^{-10} = \frac{1}{9^{10}} \] Therefore, \[ 429 \cdot 9^{-10} = \frac{429}{9^{10}} \] Thus, our expression becomes: \[ -2185 - \frac{429}{9^{10}} \]
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There isn't a need to combine these further, especially since we want only positive exponents.
Therefore, the simplified expression with only positive exponents is: \[ -2185 - \frac{429}{9^{10}} \]
In your options you mentioned \(2392\), but this does not match our derived expression. Please double-check the expressions provided for equivalency, or confirm if \(2392\) has been derived correctly from given values.
So the answer, as derived from the provided expression, does not equal to \(2392\). If you need further clarification on any of the steps, let me know!