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, 29=18, which is not in exponent form.

B. 33+34

  • This involves adding two negative exponents.
  • We know that 33=133 and 34=134, so this is not a single positive exponent.

C. 32(35)

  • Using the property of exponents aman=am+n:
  • 3235=32+(5)=33, which is still a negative exponent.

D. 31137

  • Using the property of exponents aman=amn:
  • This simplifies to 311(7)=311+7=34, 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.