Which expression simplified would leave you with a positive exponent when simplified in exponent form?

A. -2(-3)^2
B. 3^-3 + 3^-4
C. 3^2 (3^-5)
D. 3^-11/3^-7

1 answer

To determine which expression would simplify to a positive exponent, let's evaluate each option:

A. \(-2(-3)^2\)

  • \((-3)^2 = 9\)
  • So, \(-2 \cdot 9 = -18\), which is not in exponent form.

B. \(3^{-3} + 3^{-4}\)

  • This involves adding two negative exponents.
  • We know that \(3^{-3} = \frac{1}{3^3}\) and \(3^{-4} = \frac{1}{3^4}\), so this is not a single positive exponent.

C. \(3^{2} (3^{-5})\)

  • Using the property of exponents \(a^m \cdot a^n = a^{m+n}\):
  • \(3^{2} \cdot 3^{-5} = 3^{2 + (-5)} = 3^{-3}\), which is still a negative exponent.

D. \(\frac{3^{-11}}{3^{-7}}\)

  • Using the property of exponents \( \frac{a^m}{a^n} = a^{m-n} \):
  • This simplifies to \(3^{-11 - (-7)} = 3^{-11 + 7} = 3^{-4}\), which is also a negative exponent.

After evaluating all options, none of the choices provided simplify to a positive exponent. However, if "which expression" implies looking for something that doesn't directly imply a positive exponent but has the potential to reach positive results based on operations, D would be the best consideration since it revolves around manipulating exponents, but ultimately, all options present negative or non-exponential forms from calculations.