Solve 10.344div0.13div(1-1div1.13^2)

$$10.344 \div 0.13 \div (1-1 \div { 1.13 }^{ 2 } )$$

Evaluate

$$\frac{22013756}{59995}\approx 366.926510543$$

Solution Steps

Expand \frac{10.344}{0.13} by multiplying both numerator and the denominator by 1000.

$$\frac{\frac{10344}{130}}{1-\frac{1}{1.13^{2}}}$$

Reduce the fraction \frac{10344}{130} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{5172}{65}}{1-\frac{1}{1.13^{2}}}$$

Calculate 1.13 to the power of 2 and get 1.2769.

$$\frac{\frac{5172}{65}}{1-\frac{1}{1.2769}}$$

Expand \frac{1}{1.2769} by multiplying both numerator and the denominator by 10000.

$$\frac{\frac{5172}{65}}{1-\frac{10000}{12769}}$$

Convert 1 to fraction \frac{12769}{12769}.

$$\frac{\frac{5172}{65}}{\frac{12769}{12769}-\frac{10000}{12769}}$$

Since \frac{12769}{12769} and \frac{10000}{12769} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5172}{65}}{\frac{12769-10000}{12769}}$$

Subtract 10000 from 12769 to get 2769.

$$\frac{\frac{5172}{65}}{\frac{2769}{12769}}$$

Divide \frac{5172}{65} by \frac{2769}{12769} by multiplying \frac{5172}{65} by the reciprocal of \frac{2769}{12769}.

$$\frac{5172}{65}\times \frac{12769}{2769}$$

Multiply \frac{5172}{65} times \frac{12769}{2769} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5172\times 12769}{65\times 2769}$$

Do the multiplications in the fraction \frac{5172\times 12769}{65\times 2769}.

$$\frac{66041268}{179985}$$

Reduce the fraction \frac{66041268}{179985} to lowest terms by extracting and canceling out 3.

$$\frac{22013756}{59995}$$

Factor

$$\frac{431 \cdot 2 ^ {2} \cdot 113 ^ {2}}{5 \cdot 71 \cdot 13 ^ {2}} = 366\frac{55586}{59995} = 366.9265105425452$$