Solve [-(2)^-4+5/2(2)^-3]-[-(1)^-4+5/2(1)^-5]

$$[ - ( 2 ) ^ { - 4 } + \frac { 5 } { 2 } ( 2 ) ^ { - 3 } ] - [ - ( 1 ) ^ { - 4 } + \frac { 5 } { 2 } ( 1 ) ^ { - 5 } ]$$

Evaluate

$$-\frac{5}{4}=-1.25$$

Solution Steps

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

$$-\frac{1}{16}+\frac{5}{2}\times 2^{-3}-\left(-1^{-4}+\frac{5}{2}\times 1^{-5}\right)$$

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

$$-\frac{1}{16}+\frac{5}{2}\times \frac{1}{8}-\left(-1^{-4}+\frac{5}{2}\times 1^{-5}\right)$$

Multiply \frac{5}{2} and \frac{1}{8} to get \frac{5}{16}.

$$-\frac{1}{16}+\frac{5}{16}-\left(-1^{-4}+\frac{5}{2}\times 1^{-5}\right)$$

Add -\frac{1}{16} and \frac{5}{16} to get \frac{1}{4}.

$$\frac{1}{4}-\left(-1^{-4}+\frac{5}{2}\times 1^{-5}\right)$$

Calculate 1 to the power of -4 and get 1.

$$\frac{1}{4}-\left(-1+\frac{5}{2}\times 1^{-5}\right)$$

Calculate 1 to the power of -5 and get 1.

$$\frac{1}{4}-\left(-1+\frac{5}{2}\times 1\right)$$

Multiply \frac{5}{2} and 1 to get \frac{5}{2}.

$$\frac{1}{4}-\left(-1+\frac{5}{2}\right)$$

Add -1 and \frac{5}{2} to get \frac{3}{2}.

$$\frac{1}{4}-\frac{3}{2}$$

Subtract \frac{3}{2} from \frac{1}{4} to get -\frac{5}{4}.

$$-\frac{5}{4}$$

Factor

$$-\frac{5}{4} = -1\frac{1}{4} = -1.25$$