Solve (-2)^{-2}+(-2)^-1*(-2)^3+3^2-(-2)^4

$$( - 2 ) ^ { - 2 } + ( - 2 ) ^ { - 1 } \cdot ( - 2 ) ^ { 3 } + 3 ^ { 2 } - ( - 2 ) ^ { 4 }$$

Evaluate

$$-\frac{11}{4}=-2.75$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and 3 to get 2.

$$\left(-2\right)^{-2}+\left(-2\right)^{2}+3^{2}-\left(-2\right)^{4}$$

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

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

Calculate -2 to the power of 2 and get 4.

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

Add \frac{1}{4} and 4 to get \frac{17}{4}.

$$\frac{17}{4}+3^{2}-\left(-2\right)^{4}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{17}{4}+9-\left(-2\right)^{4}$$

Add \frac{17}{4} and 9 to get \frac{53}{4}.

$$\frac{53}{4}-\left(-2\right)^{4}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{53}{4}-16$$

Subtract 16 from \frac{53}{4} to get -\frac{11}{4}.

$$-\frac{11}{4}$$

Factor

$$-\frac{11}{4} = -2\frac{3}{4} = -2.75$$