Solve 12^5-3^-5*10^-5/5-7*6^-5

$$\frac { 12 ^ { 5 } - 3 ^ { - 5 } \times 10 ^ { - 5 } } { 5 - 7 \times 6 ^ { - 5 } }$$

Evaluate

$$\frac{6046617599999}{121478125}\approx 49775.361613451$$

Solution Steps

Calculate 12 to the power of 5 and get 248832.

$$\frac{248832-3^{-5}\times 10^{-5}}{5-7\times 6^{-5}}$$

Calculate 3 to the power of -5 and get \frac{1}{243}.

$$\frac{248832-\frac{1}{243}\times 10^{-5}}{5-7\times 6^{-5}}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\frac{248832-\frac{1}{243}\times \frac{1}{100000}}{5-7\times 6^{-5}}$$

Multiply \frac{1}{243} and \frac{1}{100000} to get \frac{1}{24300000}.

$$\frac{248832-\frac{1}{24300000}}{5-7\times 6^{-5}}$$

Subtract \frac{1}{24300000} from 248832 to get \frac{6046617599999}{24300000}.

$$\frac{\frac{6046617599999}{24300000}}{5-7\times 6^{-5}}$$

Calculate 6 to the power of -5 and get \frac{1}{7776}.

$$\frac{\frac{6046617599999}{24300000}}{5-7\times \frac{1}{7776}}$$

Multiply 7 and \frac{1}{7776} to get \frac{7}{7776}.

$$\frac{\frac{6046617599999}{24300000}}{5-\frac{7}{7776}}$$

Subtract \frac{7}{7776} from 5 to get \frac{38873}{7776}.

$$\frac{\frac{6046617599999}{24300000}}{\frac{38873}{7776}}$$

Divide \frac{6046617599999}{24300000} by \frac{38873}{7776} by multiplying \frac{6046617599999}{24300000} by the reciprocal of \frac{38873}{7776}.

$$\frac{6046617599999}{24300000}\times \frac{7776}{38873}$$

Multiply \frac{6046617599999}{24300000} and \frac{7776}{38873} to get \frac{6046617599999}{121478125}.

$$\frac{6046617599999}{121478125}$$

Factor

$$\frac{71 \cdot 359 \cdot 237224591}{5 ^ {5} \cdot 38873} = 49775\frac{43928124}{121478125} = 49775.36161345098$$