Solve [(1/2)^{4}+(1/2)^{2}-(1/4)^2*3]^2:(1/2)^2+frac{3}{16}+(frac{1}{2})^2

$$[ ( \frac { 1 } { 2 } ) ^ { 4 } + ( \frac { 1 } { 2 } ) ^ { 2 } - ( \frac { 1 } { 4 } ) ^ { 2 } \times 3 ] ^ { 2 } : ( \frac { 1 } { 2 } ) ^ { 2 } + \frac { 3 } { 16 } + ( \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

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

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

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

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

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

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

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

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

Multiply \frac{1}{16} and 3 to get \frac{3}{16}.

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

Subtract \frac{3}{16} from \frac{5}{16} to get \frac{1}{8}.

$$\frac{\left(\frac{1}{8}\right)^{2}}{\left(\frac{1}{2}\right)^{2}}+\frac{3}{16}+\left(\frac{1}{2}\right)^{2}$$

Calculate \frac{1}{8} to the power of 2 and get \frac{1}{64}.

$$\frac{\frac{1}{64}}{\left(\frac{1}{2}\right)^{2}}+\frac{3}{16}+\left(\frac{1}{2}\right)^{2}$$

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

$$\frac{\frac{1}{64}}{\frac{1}{4}}+\frac{3}{16}+\left(\frac{1}{2}\right)^{2}$$

Divide \frac{1}{64} by \frac{1}{4} by multiplying \frac{1}{64} by the reciprocal of \frac{1}{4}.

$$\frac{1}{64}\times 4+\frac{3}{16}+\left(\frac{1}{2}\right)^{2}$$

Multiply \frac{1}{64} and 4 to get \frac{1}{16}.

$$\frac{1}{16}+\frac{3}{16}+\left(\frac{1}{2}\right)^{2}$$

Add \frac{1}{16} and \frac{3}{16} to get \frac{1}{4}.

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

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

$$\frac{1}{4}+\frac{1}{4}$$

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

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$