To determine which expression can be generated by applying the properties of integer exponents, let's analyze the given choices.
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2392
- This is a numerical value, not an expression involving exponents, so it does not apply.
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Start Fraction 2 cubed over 9 squared end fraction
- This can be expressed as \(\frac{2^3}{9^2}\), representing a basic fractional expression with exponents.
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212⋅9−1229⋅9−10
- This can be simplified using exponent rules: \[ \frac{2^{12} \cdot 9^{-12}}{2^{9} \cdot 9^{-10}} = \frac{2^{12-9} \cdot 9^{-12 - (-10)}}{1} = 2^3 \cdot 9^{-2} \]
- This expression utilizes exponent rules effectively.
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Start Fraction 2 superscript 12 baseline times 9 superscript negative 12 baseline over 2 superscript 9 baseline times 9 superscript negative 10 baseline
- Similar to the previous analysis, when simplified, it leads back to using properties of exponents, showing it can be reduced to a simpler form like \(2^3 \cdot 9^{-2}\).
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23 ⋅92
- This is simply \(2^3 \cdot 9^2\), which is just a multiplication of terms with exponents, not showing any manipulation or application of exponent properties.
Thus, the expression that clearly shows the application of properties of integer exponents is the one that involves simplification:
212⋅9−1229⋅9−10
This expression explicitly applies properties of integer exponents through simplification, which is a key characteristic when we talk about generating expressions via exponent rules.
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