Solve (-2)^4=(-22/3)^2+51/2*(-1/6)-1/4

$$( - 2 ) ^ { 4 } = ( - 2 \frac { 2 } { 3 } ) ^ { 2 } + 5 \frac { 1 } { 2 } \times ( - \frac { 1 } { 6 } ) - \frac { 1 } { 4 }$$

Verify

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 2,6,4.

$$12\left(-2\right)^{4}=12\left(-\frac{2\times 3+2}{3}\right)^{2}+6\left(5\times 2+1\right)\left(-\frac{1}{6}\right)-3$$

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

$$12\times 16=12\left(-\frac{2\times 3+2}{3}\right)^{2}+6\left(5\times 2+1\right)\left(-\frac{1}{6}\right)-3$$

Multiply 12 and 16 to get 192.

$$192=12\left(-\frac{2\times 3+2}{3}\right)^{2}+6\left(5\times 2+1\right)\left(-\frac{1}{6}\right)-3$$

Multiply 2 and 3 to get 6.

$$192=12\left(-\frac{6+2}{3}\right)^{2}+6\left(5\times 2+1\right)\left(-\frac{1}{6}\right)-3$$

Add 6 and 2 to get 8.

$$192=12\left(-\frac{8}{3}\right)^{2}+6\left(5\times 2+1\right)\left(-\frac{1}{6}\right)-3$$

Calculate -\frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$192=12\times \frac{64}{9}+6\left(5\times 2+1\right)\left(-\frac{1}{6}\right)-3$$

Multiply 12 and \frac{64}{9} to get \frac{256}{3}.

$$192=\frac{256}{3}+6\left(5\times 2+1\right)\left(-\frac{1}{6}\right)-3$$

Multiply 5 and 2 to get 10.

$$192=\frac{256}{3}+6\left(10+1\right)\left(-\frac{1}{6}\right)-3$$

Add 10 and 1 to get 11.

$$192=\frac{256}{3}+6\times 11\left(-\frac{1}{6}\right)-3$$

Multiply 6 and 11 to get 66.

$$192=\frac{256}{3}+66\left(-\frac{1}{6}\right)-3$$

Multiply 66 and -\frac{1}{6} to get -11.

$$192=\frac{256}{3}-11-3$$

Subtract 11 from \frac{256}{3} to get \frac{223}{3}.

$$192=\frac{223}{3}-3$$

Subtract 3 from \frac{223}{3} to get \frac{214}{3}.

$$192=\frac{214}{3}$$

Convert 192 to fraction \frac{576}{3}.

$$\frac{576}{3}=\frac{214}{3}$$

Compare \frac{576}{3} and \frac{214}{3}.

$$\text{false}$$