Solve 5*(4^2-left(2^3right)^5/(2*{left(4^2right)^4}

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

Evaluate

$$-\frac{10235}{8192}=-1.249389648$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$5\times \frac{4^{2}-2^{15}}{2\times \left(4^{2}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$5\times \frac{4^{2}-2^{15}}{2\times 4^{8}}$$

Calculate 4 to the power of 2 and get 16.

$$5\times \frac{16-2^{15}}{2\times 4^{8}}$$

Calculate 2 to the power of 15 and get 32768.

$$5\times \frac{16-32768}{2\times 4^{8}}$$

Subtract 32768 from 16 to get -32752.

$$5\times \frac{-32752}{2\times 4^{8}}$$

Calculate 4 to the power of 8 and get 65536.

$$5\times \frac{-32752}{2\times 65536}$$

Multiply 2 and 65536 to get 131072.

$$5\times \frac{-32752}{131072}$$

Reduce the fraction \frac{-32752}{131072} to lowest terms by extracting and canceling out 16.

$$5\left(-\frac{2047}{8192}\right)$$

Multiply 5 and -\frac{2047}{8192} to get -\frac{10235}{8192}.

$$-\frac{10235}{8192}$$

Factor

$$-\frac{10235}{8192} = -1\frac{2043}{8192} = -1.2493896484375$$