Solve 5/2+(frac{2*-3^{-2}}{2-1})^{-2}+-3*4^-1+1+2*4^-2/4^-1-2*4^-2

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

Evaluate

$$\frac{103}{4}=25.75$$

Solution Steps

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

$$\frac{5}{2}+\left(\frac{2\left(-\frac{1}{9}\right)}{2-1}\right)^{-2}+\frac{-3\times 4^{-1}+1+2\times 4^{-2}}{4^{-1}-2\times 4^{-2}}$$

Multiply 2 and -\frac{1}{9} to get -\frac{2}{9}.

$$\frac{5}{2}+\left(\frac{-\frac{2}{9}}{2-1}\right)^{-2}+\frac{-3\times 4^{-1}+1+2\times 4^{-2}}{4^{-1}-2\times 4^{-2}}$$

Subtract 1 from 2 to get 1.

$$\frac{5}{2}+\left(\frac{-\frac{2}{9}}{1}\right)^{-2}+\frac{-3\times 4^{-1}+1+2\times 4^{-2}}{4^{-1}-2\times 4^{-2}}$$

Anything divided by one gives itself.

$$\frac{5}{2}+\left(-\frac{2}{9}\right)^{-2}+\frac{-3\times 4^{-1}+1+2\times 4^{-2}}{4^{-1}-2\times 4^{-2}}$$

Calculate -\frac{2}{9} to the power of -2 and get \frac{81}{4}.

$$\frac{5}{2}+\frac{81}{4}+\frac{-3\times 4^{-1}+1+2\times 4^{-2}}{4^{-1}-2\times 4^{-2}}$$

Add \frac{5}{2} and \frac{81}{4} to get \frac{91}{4}.

$$\frac{91}{4}+\frac{-3\times 4^{-1}+1+2\times 4^{-2}}{4^{-1}-2\times 4^{-2}}$$

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

$$\frac{91}{4}+\frac{-3\times \frac{1}{4}+1+2\times 4^{-2}}{4^{-1}-2\times 4^{-2}}$$

Multiply -3 and \frac{1}{4} to get -\frac{3}{4}.

$$\frac{91}{4}+\frac{-\frac{3}{4}+1+2\times 4^{-2}}{4^{-1}-2\times 4^{-2}}$$

Add -\frac{3}{4} and 1 to get \frac{1}{4}.

$$\frac{91}{4}+\frac{\frac{1}{4}+2\times 4^{-2}}{4^{-1}-2\times 4^{-2}}$$

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

$$\frac{91}{4}+\frac{\frac{1}{4}+2\times \frac{1}{16}}{4^{-1}-2\times 4^{-2}}$$

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

$$\frac{91}{4}+\frac{\frac{1}{4}+\frac{1}{8}}{4^{-1}-2\times 4^{-2}}$$

Add \frac{1}{4} and \frac{1}{8} to get \frac{3}{8}.

$$\frac{91}{4}+\frac{\frac{3}{8}}{4^{-1}-2\times 4^{-2}}$$

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

$$\frac{91}{4}+\frac{\frac{3}{8}}{\frac{1}{4}-2\times 4^{-2}}$$

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

$$\frac{91}{4}+\frac{\frac{3}{8}}{\frac{1}{4}-2\times \frac{1}{16}}$$

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

$$\frac{91}{4}+\frac{\frac{3}{8}}{\frac{1}{4}-\frac{1}{8}}$$

Subtract \frac{1}{8} from \frac{1}{4} to get \frac{1}{8}.

$$\frac{91}{4}+\frac{\frac{3}{8}}{\frac{1}{8}}$$

Divide \frac{3}{8} by \frac{1}{8} by multiplying \frac{3}{8} by the reciprocal of \frac{1}{8}.

$$\frac{91}{4}+\frac{3}{8}\times 8$$

Multiply \frac{3}{8} and 8 to get 3.

$$\frac{91}{4}+3$$

Add \frac{91}{4} and 3 to get \frac{103}{4}.

$$\frac{103}{4}$$

Factor

$$\frac{103}{2 ^ {2}} = 25\frac{3}{4} = 25.75$$