Solve 1600(1+10/2/100)^2*frac{3{2}}

$$1600 ( 1 + \frac { \frac { 10 } { 2 } } { 100 } ) ^ { 2 \times \frac { 3 } { 2 } }$$

Evaluate

$$\frac{9261}{5}=1852.2$$

Solution Steps

Express \frac{\frac{10}{2}}{100} as a single fraction.

$$1600\left(1+\frac{10}{2\times 100}\right)^{2\times \frac{3}{2}}$$

Multiply 2 and 100 to get 200.

$$1600\left(1+\frac{10}{200}\right)^{2\times \frac{3}{2}}$$

Reduce the fraction \frac{10}{200} to lowest terms by extracting and canceling out 10.

$$1600\left(1+\frac{1}{20}\right)^{2\times \frac{3}{2}}$$

Add 1 and \frac{1}{20} to get \frac{21}{20}.

$$1600\times \left(\frac{21}{20}\right)^{2\times \frac{3}{2}}$$

Multiply 2 and \frac{3}{2} to get 3.

$$1600\times \left(\frac{21}{20}\right)^{3}$$

Calculate \frac{21}{20} to the power of 3 and get \frac{9261}{8000}.

$$1600\times \frac{9261}{8000}$$

Multiply 1600 and \frac{9261}{8000} to get \frac{9261}{5}.

$$\frac{9261}{5}$$

Factor

$$\frac{3 ^ {3} \cdot 7 ^ {3}}{5} = 1852\frac{1}{5} = 1852.2$$