To find which expression simplifies to a negative exponent, let's analyze each provided option:
-
\( 3^3 - 3^4 \): Simplifying this, we have: \[ 3^3 - 3^4 = 27 - 81 = -54 \] This is a negative number, but it does not have an exponent.
-
\( (-3)^2 \): Simplifying this gives: \[ (-3)^2 = 9 \] Again, this is a positive number, not an exponent.
-
\( 3^5 \cdot (-3)^2 \): Simplifying this: \[ 3^5 \cdot (-3)^2 = 243 \cdot 9 = 2187 \] This is also a positive number, not an exponent.
-
\( 3^{33} \cdot 3^{7} \): Using the property of exponents: \[ 3^{33} \cdot 3^{7} = 3^{33 + 7} = 3^{40} \] This is still a positive exponent.
None of the expressions provided produce a negative exponent when simplified.
However, to introduce negative exponents, you would typically have a division structure such as \( \frac{1}{3^2} \), which would simplify to \( 3^{-2} \).
From the provided options, it seems there might be a misunderstanding of which expressions were properly analyzed since none yield a negative exponent. Please verify if there are any missing details or different options to consider.
1 answer