To determine which expression simplifies to a negative exponent, let's analyze each option:
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\(3^3 - 3^4\)
- This simplifies to \(3^3(1 - 3) = 3^3(-2)\), which does not involve exponents in the simplification.
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\(\frac{3^3}{3^7}\)
- Using the quotient rule \(a^m / a^n = a^{m-n}\), this simplifies to \(3^{3-7} = 3^{-4}\). This does have a negative exponent.
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\(3^5 \cdot (-3)^2\)
- This simplifies to \(3^5 \cdot 9\), which is positive, as both components are positive numbers.
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\((-3)^2\)
- This simplifies to \(9\), which is also positive.
The expression that, when simplified, results in a negative exponent is:
\(\frac{3^3}{3^7}\) (which simplifies to \(3^{-4}\)).
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