Solve 10,000(1+8/4/100)^frac{3{4}*4}

$$10,000 ( 1 + \frac { \frac { 8 } { 4 } } { 100 } ) ^ { \frac { 3 } { 4 } \times 4 }$$

Evaluate

$$\frac{265302}{25}=10612.08$$

Solution Steps

Express \frac{\frac{8}{4}}{100} as a single fraction.

$$10000\left(1+\frac{8}{4\times 100}\right)^{\frac{3}{4}\times 4}$$

Multiply 4 and 100 to get 400.

$$10000\left(1+\frac{8}{400}\right)^{\frac{3}{4}\times 4}$$

Reduce the fraction \frac{8}{400} to lowest terms by extracting and canceling out 8.

$$10000\left(1+\frac{1}{50}\right)^{\frac{3}{4}\times 4}$$

Add 1 and \frac{1}{50} to get \frac{51}{50}.

$$10000\times \left(\frac{51}{50}\right)^{\frac{3}{4}\times 4}$$

Multiply \frac{3}{4} and 4 to get 3.

$$10000\times \left(\frac{51}{50}\right)^{3}$$

Calculate \frac{51}{50} to the power of 3 and get \frac{132651}{125000}.

$$10000\times \frac{132651}{125000}$$

Multiply 10000 and \frac{132651}{125000} to get \frac{265302}{25}.

$$\frac{265302}{25}$$

Factor

$$\frac{2 \cdot 3 ^ {3} \cdot 17 ^ {3}}{5 ^ {2}} = 10612\frac{2}{25} = 10612.08$$