Solve (1/2)^{2}+[(-1/4)^6:(-1/2)^6]:(1/2)^4+(frac{1}{4}+frac{1}{2})^0*(1-frac{1}{2})

$$( \frac { 1 } { 2 } ) ^ { 2 } + [ ( - \frac { 1 } { 4 } ) ^ { 6 } : ( - \frac { 1 } { 2 } ) ^ { 6 } ] : ( \frac { 1 } { 2 } ) ^ { 4 } + ( \frac { 1 } { 4 } + \frac { 1 } { 2 } ) ^ { 0 } \cdot ( 1 - \frac { 1 } { 2 } )$$

Evaluate

$$1$$

Solution Steps

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

$$\frac{1}{4}+\frac{\frac{\left(-\frac{1}{4}\right)^{6}}{\left(-\frac{1}{2}\right)^{6}}}{\left(\frac{1}{2}\right)^{4}}+\left(\frac{1}{4}+\frac{1}{2}\right)^{0}\left(1-\frac{1}{2}\right)$$

Calculate -\frac{1}{4} to the power of 6 and get \frac{1}{4096}.

$$\frac{1}{4}+\frac{\frac{\frac{1}{4096}}{\left(-\frac{1}{2}\right)^{6}}}{\left(\frac{1}{2}\right)^{4}}+\left(\frac{1}{4}+\frac{1}{2}\right)^{0}\left(1-\frac{1}{2}\right)$$

Calculate -\frac{1}{2} to the power of 6 and get \frac{1}{64}.

$$\frac{1}{4}+\frac{\frac{\frac{1}{4096}}{\frac{1}{64}}}{\left(\frac{1}{2}\right)^{4}}+\left(\frac{1}{4}+\frac{1}{2}\right)^{0}\left(1-\frac{1}{2}\right)$$

Divide \frac{1}{4096} by \frac{1}{64} by multiplying \frac{1}{4096} by the reciprocal of \frac{1}{64}.

$$\frac{1}{4}+\frac{\frac{1}{4096}\times 64}{\left(\frac{1}{2}\right)^{4}}+\left(\frac{1}{4}+\frac{1}{2}\right)^{0}\left(1-\frac{1}{2}\right)$$

Multiply \frac{1}{4096} and 64 to get \frac{1}{64}.

$$\frac{1}{4}+\frac{\frac{1}{64}}{\left(\frac{1}{2}\right)^{4}}+\left(\frac{1}{4}+\frac{1}{2}\right)^{0}\left(1-\frac{1}{2}\right)$$

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

$$\frac{1}{4}+\frac{\frac{1}{64}}{\frac{1}{16}}+\left(\frac{1}{4}+\frac{1}{2}\right)^{0}\left(1-\frac{1}{2}\right)$$

Divide \frac{1}{64} by \frac{1}{16} by multiplying \frac{1}{64} by the reciprocal of \frac{1}{16}.

$$\frac{1}{4}+\frac{1}{64}\times 16+\left(\frac{1}{4}+\frac{1}{2}\right)^{0}\left(1-\frac{1}{2}\right)$$

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

$$\frac{1}{4}+\frac{1}{4}+\left(\frac{1}{4}+\frac{1}{2}\right)^{0}\left(1-\frac{1}{2}\right)$$

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

$$\frac{1}{2}+\left(\frac{1}{4}+\frac{1}{2}\right)^{0}\left(1-\frac{1}{2}\right)$$

Add \frac{1}{4} and \frac{1}{2} to get \frac{3}{4}.

$$\frac{1}{2}+\left(\frac{3}{4}\right)^{0}\left(1-\frac{1}{2}\right)$$

Calculate \frac{3}{4} to the power of 0 and get 1.

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

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$\frac{1}{2}+1\times \frac{1}{2}$$

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

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

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

$$1$$

Factor

$$1$$