Solve frac{2^0+2^32^2+{left(2^3right)}^2-2}{2{2}^2}+{2}^-3

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

Evaluate

$$12$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{2^{0}+2^{5}+\left(2^{3}\right)^{2}-2}{2\times 2^{2}}+2^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{2^{0}+2^{5}+2^{6}-2}{2\times 2^{2}}+2^{-3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{2^{0}+2^{5}+2^{6}-2}{2^{3}}+2^{-3}$$

Calculate 2 to the power of 0 and get 1.

$$\frac{1+2^{5}+2^{6}-2}{2^{3}}+2^{-3}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{1+32+2^{6}-2}{2^{3}}+2^{-3}$$

Add 1 and 32 to get 33.

$$\frac{33+2^{6}-2}{2^{3}}+2^{-3}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{33+64-2}{2^{3}}+2^{-3}$$

Add 33 and 64 to get 97.

$$\frac{97-2}{2^{3}}+2^{-3}$$

Subtract 2 from 97 to get 95.

$$\frac{95}{2^{3}}+2^{-3}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{95}{8}+2^{-3}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{95}{8}+\frac{1}{8}$$

Add \frac{95}{8} and \frac{1}{8} to get 12.

$$12$$

Factor

$$2^{2}\times 3$$