Solve -[1/2(frac{-1}4^4+1^3-4)]-[1/2(-2^4/4+2^3-8)]

$$- [ \frac { 1 } { 2 } ( \frac { - 1 } { 4 } ^ { 4 } + 1 ^ { 3 } - 4 ) ] - [ \frac { 1 } { 2 } ( \frac { - 2 ^ { 4 } } { 4 } + 2 ^ { 3 } - 8 ) ]$$

Evaluate

$$\frac{1791}{512}=3.498046875$$

Solution Steps

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$-\frac{1}{2}\left(\left(-\frac{1}{4}\right)^{4}+1^{3}-4\right)-\frac{1}{2}\left(\frac{-2^{4}}{4}+2^{3}-8\right)$$

Calculate -\frac{1}{4} to the power of 4 and get \frac{1}{256}.

$$-\frac{1}{2}\left(\frac{1}{256}+1^{3}-4\right)-\frac{1}{2}\left(\frac{-2^{4}}{4}+2^{3}-8\right)$$

Calculate 1 to the power of 3 and get 1.

$$-\frac{1}{2}\left(\frac{1}{256}+1-4\right)-\frac{1}{2}\left(\frac{-2^{4}}{4}+2^{3}-8\right)$$

Add \frac{1}{256} and 1 to get \frac{257}{256}.

$$-\frac{1}{2}\left(\frac{257}{256}-4\right)-\frac{1}{2}\left(\frac{-2^{4}}{4}+2^{3}-8\right)$$

Subtract 4 from \frac{257}{256} to get -\frac{767}{256}.

$$-\frac{1}{2}\left(-\frac{767}{256}\right)-\frac{1}{2}\left(\frac{-2^{4}}{4}+2^{3}-8\right)$$

Multiply \frac{1}{2} and -\frac{767}{256} to get -\frac{767}{512}.

$$-\left(-\frac{767}{512}\right)-\frac{1}{2}\left(\frac{-2^{4}}{4}+2^{3}-8\right)$$

The opposite of -\frac{767}{512} is \frac{767}{512}.

$$\frac{767}{512}-\frac{1}{2}\left(\frac{-2^{4}}{4}+2^{3}-8\right)$$

Calculate 2 to the power of 4 and get 16.

$$\frac{767}{512}-\frac{1}{2}\left(\frac{-16}{4}+2^{3}-8\right)$$

Divide -16 by 4 to get -4.

$$\frac{767}{512}-\frac{1}{2}\left(-4+2^{3}-8\right)$$

Calculate 2 to the power of 3 and get 8.

$$\frac{767}{512}-\frac{1}{2}\left(-4+8-8\right)$$

Add -4 and 8 to get 4.

$$\frac{767}{512}-\frac{1}{2}\left(4-8\right)$$

Subtract 8 from 4 to get -4.

$$\frac{767}{512}-\frac{1}{2}\left(-4\right)$$

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

$$\frac{767}{512}-\left(-2\right)$$

The opposite of -2 is 2.

$$\frac{767}{512}+2$$

Add \frac{767}{512} and 2 to get \frac{1791}{512}.

$$\frac{1791}{512}$$

Factor

$$\frac{3 ^ {2} \cdot 199}{2 ^ {9}} = 3\frac{255}{512} = 3.498046875$$