Solve 3^-3*10^-3*125/5^-7*6^-5

$$\frac { 3 ^ { - 3 } \times 10 ^ { - 3 } \times 125 } { 5 ^ { - 7 } \times 6 ^ { - 5 } }$$

Evaluate

$$2812500$$

Solution Steps

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{1}{27}\times 10^{-3}\times 125}{5^{-7}\times 6^{-5}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{\frac{1}{27}\times \frac{1}{1000}\times 125}{5^{-7}\times 6^{-5}}$$

Multiply \frac{1}{27} and \frac{1}{1000} to get \frac{1}{27000}.

$$\frac{\frac{1}{27000}\times 125}{5^{-7}\times 6^{-5}}$$

Multiply \frac{1}{27000} and 125 to get \frac{1}{216}.

$$\frac{\frac{1}{216}}{5^{-7}\times 6^{-5}}$$

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

$$\frac{\frac{1}{216}}{\frac{1}{78125}\times 6^{-5}}$$

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

$$\frac{\frac{1}{216}}{\frac{1}{78125}\times \frac{1}{7776}}$$

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

$$\frac{\frac{1}{216}}{\frac{1}{607500000}}$$

Divide \frac{1}{216} by \frac{1}{607500000} by multiplying \frac{1}{216} by the reciprocal of \frac{1}{607500000}.

$$\frac{1}{216}\times 607500000$$

Multiply \frac{1}{216} and 607500000 to get 2812500.

$$2812500$$

Factor

$$2^{2}\times 3^{2}\times 5^{7}$$