Solve 2^-2/3-2(1/3)-1/4=2(1/4)=frac{9}{2}

$$\frac { 2 ^ { - 2 } } { 3 } - 2 ( \frac { 1 } { 3 } ) - \frac { 1 } { 4 } = 2 ( \frac { 1 } { 4 } ) = \frac { 9 } { 2 }$$

Verify

Solution Steps

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

$$\frac{\frac{1}{4}}{3}-2\times \frac{1}{3}-\frac{1}{4}=2\times \frac{1}{4}\text{ and }2\times \frac{1}{4}=\frac{9}{2}$$

Express \frac{\frac{1}{4}}{3} as a single fraction.

$$\frac{1}{4\times 3}-2\times \frac{1}{3}-\frac{1}{4}=2\times \frac{1}{4}\text{ and }2\times \frac{1}{4}=\frac{9}{2}$$

Multiply 4 and 3 to get 12.

$$\frac{1}{12}-2\times \frac{1}{3}-\frac{1}{4}=2\times \frac{1}{4}\text{ and }2\times \frac{1}{4}=\frac{9}{2}$$

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

$$\frac{1}{12}-\frac{2}{3}-\frac{1}{4}=2\times \frac{1}{4}\text{ and }2\times \frac{1}{4}=\frac{9}{2}$$

Subtract \frac{2}{3} from \frac{1}{12} to get -\frac{7}{12}.

$$-\frac{7}{12}-\frac{1}{4}=2\times \frac{1}{4}\text{ and }2\times \frac{1}{4}=\frac{9}{2}$$

Subtract \frac{1}{4} from -\frac{7}{12} to get -\frac{5}{6}.

$$-\frac{5}{6}=2\times \frac{1}{4}\text{ and }2\times \frac{1}{4}=\frac{9}{2}$$

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

$$-\frac{5}{6}=\frac{1}{2}\text{ and }2\times \frac{1}{4}=\frac{9}{2}$$

Least common multiple of 6 and 2 is 6. Convert -\frac{5}{6} and \frac{1}{2} to fractions with denominator 6.

$$-\frac{5}{6}=\frac{3}{6}\text{ and }2\times \frac{1}{4}=\frac{9}{2}$$

Compare -\frac{5}{6} and \frac{3}{6}.

$$\text{false}\text{ and }2\times \frac{1}{4}=\frac{9}{2}$$

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

$$\text{false}\text{ and }\frac{1}{2}=\frac{9}{2}$$

Compare \frac{1}{2} and \frac{9}{2}.

$$\text{false}\text{ and }\text{false}$$

The conjunction of \text{false} and \text{false} is \text{false}.

$$\text{false}$$