To simplify the expression \((2−3 \cdot 93)−429 \cdot 9−10\) with positive exponents, let's break it down step by step using the properties of exponents.
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We rewrite the expression, separating terms: \[ (2^{-3} \cdot 9^3)^{-4} \cdot 9^{-10} \]
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Apply the power of a power property \((a^m)^n = a^{m \cdot n}\): \[ (2^{-3})^{-4} \cdot (9^3)^{-4} \cdot 9^{-10} \] This simplifies to: \[ 2^{12} \cdot 9^{-12} \cdot 9^{-10} \]
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Combine the powers of \(9\) using the property \(a^m \cdot a^n = a^{m+n}\): \[ 2^{12} \cdot 9^{-12 - 10} = 2^{12} \cdot 9^{-22} \]
Now, to express it with only positive exponents, we can rewrite \(9^{-22}\) as \(\frac{1}{9^{22}}\): \[ \frac{2^{12}}{9^{22}} \]
So, looking at the options provided, this results in the equivalent expression: \[ \frac{2^{12}}{9^{22}} \]
Thus, the correct response is: \[ \text{Start Fraction 2 cubed over 9 squared end fraction} \] is not accurate. However, based on the work above, none of the listed options precisely match.
Among the provided options, it appears none lists \(2^{12}/9^{22}\) or something functionally equivalent, as \(2^3/9^2\) and the others do not represent our simplified form accurately. Please check if any options may have been mistyped or overlooked.