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

Question

Responses

23−24
2 cubed minus 2 to the 4th power

−2(−3)2
negative 2 times negative 3 squared

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

2(−12)/2(−6)

Answer 1

To determine which expression, when simplified, leaves a negative exponent, let's analyze each option one by one.

1. \(23−24\) (or \(2^3 - 2^4\)): This is a subtraction of two exponential values, and does not result in a negative exponent. It simplifies to \(2^3 - 2^4 = 8 - 16 = -8\).

2. \(-2(-3)^2\): This simplifies to \(-2(9) = -18\). There is no exponent involved that would result in a negative exponent.

3. \(2^5 ⋅ 2^{-2}\): Using the laws of exponents, this simplifies to \(2^{5 + (-2)} = 2^{3}\). The result is a positive exponent (3), not a negative one.

4. \(\frac{2^{-12}}{2^{-6}}\): Using the laws of exponents, specifically the rule that states \(\frac{a^m}{a^n} = a^{m-n}\), we get: \[ \frac{2^{-12}}{2^{-6}} = 2^{-12 - (-6)} = 2^{-12 + 6} = 2^{-6} \] This does give us a negative exponent (-6).

The expression that simplifies to a negative exponent is:

\(\frac{2^{-12}}{2^{-6}}\).