Solve 256({left(3/2right)}^7-1)

$$256( { \left( \frac{ 3 }{ 2 } \right) }^{ 7 } -1)$$

Evaluate

$$4118$$

Solution Steps

Calculate \frac{3}{2} to the power of 7 and get \frac{2187}{128}.

$$256\left(\frac{2187}{128}-1\right)$$

Convert 1 to fraction \frac{128}{128}.

$$256\left(\frac{2187}{128}-\frac{128}{128}\right)$$

Since \frac{2187}{128} and \frac{128}{128} have the same denominator, subtract them by subtracting their numerators.

$$256\times \frac{2187-128}{128}$$

Subtract 128 from 2187 to get 2059.

$$256\times \frac{2059}{128}$$

Express 256\times \frac{2059}{128} as a single fraction.

$$\frac{256\times 2059}{128}$$

Multiply 256 and 2059 to get 527104.

$$\frac{527104}{128}$$

Divide 527104 by 128 to get 4118.

$$4118$$

Factor

$$2\times 29\times 71$$