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

Question

Responses

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

3³/3⁷
the fraction with numerator 3 cubed and denominator 3 to the 7th power

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

(−3)²

Answer 1

To determine which expression would leave you with a negative exponent when simplified, we can evaluate each response:

1. 3³ − 3⁴: This can be factored as \(3³(1 - 3)\) and simplifies to a non-negative number (specifically, a negative number but not an exponent).

2. 3³/3⁷: This simplifies using the property of exponents \(a^m / a^n = a^{m-n}\): \[ 3³/3⁷ = 3^{3-7} = 3^{-4} \] This results in a negative exponent.

3. 3⁵ ⋅ (−3)²: This simplifies to: \[ 3⁵ ⋅ 9 = 3⁵ ⋅ 3² = 3^{5+2} = 3⁷ \] This results in a positive exponent.

4. (−3)²: This evaluates to: \[ 9 \] which is a positive number.

From this analysis, the expression that results in a negative exponent is:

3³/3⁷.