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

Question

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

GPT-4o mini · 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.