Question

Which expression, when simplified, would leave you with a negative exponent?

Responses:

3^3 − 3^4

3^3 over 3^7

3^5 ⋅ (−3)^2

(−3)^2

Answer 1

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

1. **\(3^3 - 3^4\)**
- This simplifies to \(3^3(1 - 3) = 3^3(-2)\), which does not involve exponents in the simplification.

2. **\(\frac{3^3}{3^7}\)**
- Using the quotient rule \(a^m / a^n = a^{m-n}\), this simplifies to \(3^{3-7} = 3^{-4}\). This does have a negative exponent.

3. **\(3^5 \cdot (-3)^2\)**
- This simplifies to \(3^5 \cdot 9\), which is positive, as both components are positive numbers.

4. **\((-3)^2\)**
- This simplifies to \(9\), which is also positive.

The expression that, when simplified, results in a negative exponent is:

**\(\frac{3^3}{3^7}\)** (which simplifies to \(3^{-4}\)).