Solve frac{3^{-6}*10^-5*12^5}{5^-7*6^-5}

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

Evaluate

$$2073600$$

Solution Steps

Calculate 3 to the power of -6 and get \frac{1}{729}.

$$\frac{\frac{1}{729}\times 10^{-5}\times 12^{5}}{5^{-7}\times 6^{-5}}$$

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

$$\frac{\frac{1}{729}\times \frac{1}{100000}\times 12^{5}}{5^{-7}\times 6^{-5}}$$

Multiply \frac{1}{729} and \frac{1}{100000} to get \frac{1}{72900000}.

$$\frac{\frac{1}{72900000}\times 12^{5}}{5^{-7}\times 6^{-5}}$$

Calculate 12 to the power of 5 and get 248832.

$$\frac{\frac{1}{72900000}\times 248832}{5^{-7}\times 6^{-5}}$$

Multiply \frac{1}{72900000} and 248832 to get \frac{32}{9375}.

$$\frac{\frac{32}{9375}}{5^{-7}\times 6^{-5}}$$

Calculate 5 to the power of -7 and get \frac{1}{78125}.

$$\frac{\frac{32}{9375}}{\frac{1}{78125}\times 6^{-5}}$$

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

$$\frac{\frac{32}{9375}}{\frac{1}{78125}\times \frac{1}{7776}}$$

Multiply \frac{1}{78125} and \frac{1}{7776} to get \frac{1}{607500000}.

$$\frac{\frac{32}{9375}}{\frac{1}{607500000}}$$

Divide \frac{32}{9375} by \frac{1}{607500000} by multiplying \frac{32}{9375} by the reciprocal of \frac{1}{607500000}.

$$\frac{32}{9375}\times 607500000$$

Multiply \frac{32}{9375} and 607500000 to get 2073600.

$$2073600$$

Factor

$$2^{10}\times 3^{4}\times 5^{2}$$