Solve 8192left({left(1+12.5/100*2right)}^3-1right)

$$8192 \left( { \left(1+ \frac{ 12.5 }{ 100 \cdot 2 } \right) }^{ 3 } -1 \right)$$

Evaluate

$$1634$$

Solution Steps

Multiply 100 and 2 to get 200.

$$8192\left(\left(1+\frac{12.5}{200}\right)^{3}-1\right)$$

Expand \frac{12.5}{200} by multiplying both numerator and the denominator by 10.

$$8192\left(\left(1+\frac{125}{2000}\right)^{3}-1\right)$$

Reduce the fraction \frac{125}{2000} to lowest terms by extracting and canceling out 125.

$$8192\left(\left(1+\frac{1}{16}\right)^{3}-1\right)$$

Add 1 and \frac{1}{16} to get \frac{17}{16}.

$$8192\left(\left(\frac{17}{16}\right)^{3}-1\right)$$

Calculate \frac{17}{16} to the power of 3 and get \frac{4913}{4096}.

$$8192\left(\frac{4913}{4096}-1\right)$$

Subtract 1 from \frac{4913}{4096} to get \frac{817}{4096}.

$$8192\times \frac{817}{4096}$$

Multiply 8192 and \frac{817}{4096} to get 1634.

$$1634$$

Factor

$$2\times 19\times 43$$