Question

Which expression, when simplified, would leave you with a negative exponent?(1 point)
Responses

35⋅(−3)2
3 to the 5th power times negative 3 squared

(−3)2
negative 3 squared

33−34
3 cubed minus 3 to the 4th power

Answer 1

To determine which expression, when simplified, would leave you with a negative exponent, let's simplify each option:

1. \( 35 \cdot (-3)^2 \)
This simplifies to \( 35 \cdot 9 = 315 \). There are no exponents in the final result, so this does not yield a negative exponent.

2. \( (-3)^2 \)
This simplifies to \( 9 \). Again, there is no exponent in the final result, so this does not yield a negative exponent.

3. \( 3^3 - 3^4 \)
This simplifies as follows:
\[
3^3 = 27
\]
\[
3^4 = 81
\]
Therefore, \( 3^3 - 3^4 = 27 - 81 = -54 \). There are no exponents in the final result, so this does not yield a negative exponent.

Among the options given, none of them simplify to give you a negative exponent.

However, in some interpretations, the expression \( 33−34 \) could be rewritten in terms of exponents:
\[
3^3 - 3^4 = 3^3(1 - 3) = 3^3(-2)
\]
But this does not result in a negative exponent either, just a negative coefficient.

If the expression were rewritten as a fraction, \( \frac{3^3}{3^4} \) would yield \( 3^{-1} \), but this isn't one of the provided options.

So, the answer is that none of the provided expressions result in negative exponents upon simplification. If you meant to include a division or a specific fraction that could yield a negative exponent, that would be a different case.