To find which expression simplifies to a positive exponent, let's analyze each option:
-
−2(−3)²
- Here, \((-3)^2 = 9\), so the expression simplifies to \(-2 \times 9 = -18\).
- This does not involve exponents in the final answer.
-
3^(−3) + 3^(−4)
- Both terms have negative exponents, so we can rewrite this as: \[ \frac{1}{3^3} + \frac{1}{3^4} = \frac{1}{27} + \frac{1}{81} \]
- This results in a positive value, but the exponents themselves are negative.
-
3²(3^(−5))
- Using the rule of exponents (\(a^m \cdot a^n = a^{m+n}\)): \[ 3^2 \cdot 3^{-5} = 3^{2-5} = 3^{-3} \]
- This gives us a negative exponent.
-
3^(−11) / 3^7
- Using the rule of division with exponents (\(a^m / a^n = a^{m-n}\)): \[ 3^{-11} / 3^7 = 3^{-11-7} = 3^{-18} \]
- This also results in a negative exponent.
Based on the analysis, none of these options directly simplify to a positive exponent. However, if the question is strictly looking for the expression that behaves closest to yielding positive results when fractions are calculated, but not on exponents itself, Option 2 (3^(−3) + 3^(−4)) provides a positive result overall, even though it still involves negative exponents.
Thus, none of these expressions yield a strictly positive exponent after simplification. However, if just judging by summing fractions with negative exponents, it can be argued that Option 2 is the least obstructive in terms of resulting in a positive outcome (this clarification is essential based on the nature of the question).
If you're seeking an expression that results in a positive exponent, you'd need to provide one where negative and positive exponents result in a net positive exponent. As it stands, none of the given choices fit that description.
1 answer