Solve -frac{-2left(2^2-12right){e}^-{left(-frac{2{8}right)}^2}}{32}

$$- \frac{ -2 \left( { 2 }^{ 2 } -12 \right) { e }^{ - { \left(- \frac{ 2 }{ 8 } \right) }^{ 2 } } }{ 32 }$$

Evaluate

$$-\frac{1}{2\sqrt[16]{e}}\approx -0.469706531$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$-\frac{-2\left(4-12\right)e^{-\left(-\frac{2}{8}\right)^{2}}}{32}$$

Subtract 12 from 4 to get -8.

$$-\frac{-2\left(-8\right)e^{-\left(-\frac{2}{8}\right)^{2}}}{32}$$

Multiply -2 and -8 to get 16.

$$-\frac{16e^{-\left(-\frac{2}{8}\right)^{2}}}{32}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{16e^{-\left(-\frac{1}{4}\right)^{2}}}{32}$$

Calculate -\frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$-\frac{16e^{-\frac{1}{16}}}{32}$$

Divide 16e^{-\frac{1}{16}} by 32 to get \frac{1}{2}e^{-\frac{1}{16}}.

$$-\frac{1}{2}e^{-\frac{1}{16}}$$