Solve 2^2+2^2+2^2+2^3+{2}^-2+{2}^2+{2}^2+{2}^-4

$${ 2 }^{ 2 } + { 2 }^{ 2 } + { 2 }^{ 2 } + { 2 }^{ 3 } + { 2 }^{ -2 } + { 2 }^{ 2 } + { 2 }^{ 2 } + { 2 }^{ -4 }$$

Evaluate

$$\frac{453}{16}=28.3125$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$4+2^{2}+2^{2}+2^{3}+2^{-2}+2^{2}+2^{2}+2^{-4}$$

Calculate 2 to the power of 2 and get 4.

$$4+4+2^{2}+2^{3}+2^{-2}+2^{2}+2^{2}+2^{-4}$$

Add 4 and 4 to get 8.

$$8+2^{2}+2^{3}+2^{-2}+2^{2}+2^{2}+2^{-4}$$

Calculate 2 to the power of 2 and get 4.

$$8+4+2^{3}+2^{-2}+2^{2}+2^{2}+2^{-4}$$

Add 8 and 4 to get 12.

$$12+2^{3}+2^{-2}+2^{2}+2^{2}+2^{-4}$$

Calculate 2 to the power of 3 and get 8.

$$12+8+2^{-2}+2^{2}+2^{2}+2^{-4}$$

Add 12 and 8 to get 20.

$$20+2^{-2}+2^{2}+2^{2}+2^{-4}$$

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

$$20+\frac{1}{4}+2^{2}+2^{2}+2^{-4}$$

Add 20 and \frac{1}{4} to get \frac{81}{4}.

$$\frac{81}{4}+2^{2}+2^{2}+2^{-4}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{81}{4}+4+2^{2}+2^{-4}$$

Add \frac{81}{4} and 4 to get \frac{97}{4}.

$$\frac{97}{4}+2^{2}+2^{-4}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{97}{4}+4+2^{-4}$$

Add \frac{97}{4} and 4 to get \frac{113}{4}.

$$\frac{113}{4}+2^{-4}$$

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

$$\frac{113}{4}+\frac{1}{16}$$

Add \frac{113}{4} and \frac{1}{16} to get \frac{453}{16}.

$$\frac{453}{16}$$

Factor

$$\frac{3 \cdot 151}{2 ^ {4}} = 28\frac{5}{16} = 28.3125$$