Question

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

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

3(3)/3(7)
the fraction with numerator 3 cubed and denominator 3 to the 7th power

(−3)2
negative 3 squared

3(5)⋅(−3)(2)

Answer 1

To determine which expression simplifies to a negative exponent, let's simplify each option:

1. **\(33−34\)**:
\[
3^3 - 3^4 = 27 - 81 = -54
\]
This results in a negative number, but not an exponent.

2. **\( \frac{3^3}{3^7} \)**:
Using the property of exponents \( \frac{a^m}{a^n} = a^{m-n} \):
\[
\frac{3^3}{3^7} = 3^{3-7} = 3^{-4}
\]
This results in a negative exponent.

3. **\((-3)^2\)**:
\[
(-3)^2 = 9
\]
This is a positive number.

4. **\(3^5 \cdot (-3)^2\)**:
First, compute \((-3)^2\):
\[
(-3)^2 = 9 \rightarrow 3^5 \cdot 9 = 3^5 \cdot 3^2 = 3^{5+2} = 3^7
\]
This results in a positive exponent.

Thus, the only expression that simplifies to a negative exponent is:

**\( \frac{3^3}{3^7} \)** (the fraction with a numerator of \( 3^3 \) and a denominator of \( 3^7 \)).