Solve 2^2(-3)^-2-(2)^-3(-4)^2

$$2 ^ { 2 } ( - 3 ) ^ { - 2 } - ( 2 ) ^ { - 3 } ( - 4 ) ^ { 2 }$$

Evaluate

$$-\frac{14}{9}\approx -1.555555556$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Calculate -3 to the power of -2 and get \frac{1}{9}.

$$4\times \frac{1}{9}-2^{-3}\left(-4\right)^{2}$$

Multiply 4 and \frac{1}{9} to get \frac{4}{9}.

$$\frac{4}{9}-2^{-3}\left(-4\right)^{2}$$

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

$$\frac{4}{9}-\frac{1}{8}\left(-4\right)^{2}$$

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

$$\frac{4}{9}-\frac{1}{8}\times 16$$

Multiply \frac{1}{8} and 16 to get 2.

$$\frac{4}{9}-2$$

Subtract 2 from \frac{4}{9} to get -\frac{14}{9}.

$$-\frac{14}{9}$$

Factor

$$-\frac{14}{9} = -1\frac{5}{9} = -1.5555555555555556$$