Solve 5*(4^2-2^15)/(2*4^8)

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

Evaluate

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

Solution Steps

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.

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

Express 5\left(-\frac{2047}{8192}\right) as a single fraction.

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

Multiply 5 and -2047 to get -10235.

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

Fraction \frac{-10235}{8192} can be rewritten as -\frac{10235}{8192} by extracting the negative sign.

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

Factor

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