Solve 400*1-{left(frac{1/2right)}^4}{1-1/2}

$$400 \times \frac{ 1- { \left( \frac{ 1 }{ 2 } \right) }^{ 4 } }{ 1- \frac{ 1 }{ 2 } }$$

Evaluate

$$750$$

Solution Steps

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

$$400\times \frac{1-\frac{1}{16}}{1-\frac{1}{2}}$$

Convert 1 to fraction \frac{16}{16}.

$$400\times \frac{\frac{16}{16}-\frac{1}{16}}{1-\frac{1}{2}}$$

Since \frac{16}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$400\times \frac{\frac{16-1}{16}}{1-\frac{1}{2}}$$

Subtract 1 from 16 to get 15.

$$400\times \frac{\frac{15}{16}}{1-\frac{1}{2}}$$

Convert 1 to fraction \frac{2}{2}.

$$400\times \frac{\frac{15}{16}}{\frac{2}{2}-\frac{1}{2}}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$400\times \frac{\frac{15}{16}}{\frac{2-1}{2}}$$

Subtract 1 from 2 to get 1.

$$400\times \frac{\frac{15}{16}}{\frac{1}{2}}$$

Divide \frac{15}{16} by \frac{1}{2} by multiplying \frac{15}{16} by the reciprocal of \frac{1}{2}.

$$400\times \frac{15}{16}\times 2$$

Express \frac{15}{16}\times 2 as a single fraction.

$$400\times \frac{15\times 2}{16}$$

Multiply 15 and 2 to get 30.

$$400\times \frac{30}{16}$$

Reduce the fraction \frac{30}{16} to lowest terms by extracting and canceling out 2.

$$400\times \frac{15}{8}$$

Express 400\times \frac{15}{8} as a single fraction.

$$\frac{400\times 15}{8}$$

Multiply 400 and 15 to get 6000.

$$\frac{6000}{8}$$

Divide 6000 by 8 to get 750.

$$750$$

Factor

$$2\times 3\times 5^{3}$$