Solve (1+0.0168)^9/(1+0.016)^9

$$\frac { ( 1 + 0.0168 ) ^ { 9 } } { ( 1 + 0.016 ) ^ { 9 } }$$

Evaluate

$$\frac{8655854647605910703754107831}{8594754748609397887000000000}\approx 1.007108975$$

Solution Steps

Add 1 and 0.0168 to get 1.0168.

$$\frac{1.0168^{9}}{\left(1+0.016\right)^{9}}$$

Calculate 1.0168 to the power of 9 and get 1.161769144699905974028757423743827968.

$$\frac{1.161769144699905974028757423743827968}{\left(1+0.016\right)^{9}}$$

Add 1 and 0.016 to get 1.016.

$$\frac{1.161769144699905974028757423743827968}{1.016^{9}}$$

Calculate 1.016 to the power of 9 and get 1.153568455075564543841140736.

$$\frac{1.161769144699905974028757423743827968}{1.153568455075564543841140736}$$

Expand \frac{1.161769144699905974028757423743827968}{1.153568455075564543841140736} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000.

$$\frac{1161769144699905974028757423743827968}{1153568455075564543841140736000000000}$$

Reduce the fraction \frac{1161769144699905974028757423743827968}{1153568455075564543841140736000000000} to lowest terms by extracting and canceling out 134217728.

$$\frac{8655854647605910703754107831}{8594754748609397887000000000}$$

Factor

$$\frac{31 ^ {9} \cdot 41 ^ {9}}{2 ^ {9} \cdot 5 ^ {9} \cdot 127 ^ {9}} = 1\frac{6.109989899651341 \times 10^{25}}{8.594754748609398 \times 10^{27}} = 1.0071089752742972$$