Solve -2^{3}-(1/2)^{-2}+[2^-1*(1/2)^-3*(-1/2)^0]^2

$$- 2 ^ { 3 } - ( \frac { 1 } { 2 } ) ^ { - 2 } + [ 2 ^ { - 1 } \times ( \frac { 1 } { 2 } ) ^ { - 3 } \times ( - \frac { 1 } { 2 } ) ^ { 0 } ] ^ { 2 }$$

Evaluate

$$4$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$-8-\left(\frac{1}{2}\right)^{-2}+\left(2^{-1}\times \left(\frac{1}{2}\right)^{-3}\left(-\frac{1}{2}\right)^{0}\right)^{2}$$

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

$$-8-4+\left(2^{-1}\times \left(\frac{1}{2}\right)^{-3}\left(-\frac{1}{2}\right)^{0}\right)^{2}$$

Subtract 4 from -8 to get -12.

$$-12+\left(2^{-1}\times \left(\frac{1}{2}\right)^{-3}\left(-\frac{1}{2}\right)^{0}\right)^{2}$$

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

$$-12+\left(\frac{1}{2}\times \left(\frac{1}{2}\right)^{-3}\left(-\frac{1}{2}\right)^{0}\right)^{2}$$

Calculate \frac{1}{2} to the power of -3 and get 8.

$$-12+\left(\frac{1}{2}\times 8\left(-\frac{1}{2}\right)^{0}\right)^{2}$$

Multiply \frac{1}{2} and 8 to get 4.

$$-12+\left(4\left(-\frac{1}{2}\right)^{0}\right)^{2}$$

Calculate -\frac{1}{2} to the power of 0 and get 1.

$$-12+\left(4\times 1\right)^{2}$$

Multiply 4 and 1 to get 4.

$$-12+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$-12+16$$

Add -12 and 16 to get 4.

$$4$$

Factor

$$2^{2}$$