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

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

Evaluate

$$\frac{20503125}{4}=5125781.25$$

Solution Steps

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

$$\frac{125\times \frac{1}{100000}\times 3^{5}}{5^{-7}\times 6^{-3}}$$

Multiply 125 and \frac{1}{100000} to get \frac{1}{800}.

$$\frac{\frac{1}{800}\times 3^{5}}{5^{-7}\times 6^{-3}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{\frac{1}{800}\times 243}{5^{-7}\times 6^{-3}}$$

Multiply \frac{1}{800} and 243 to get \frac{243}{800}.

$$\frac{\frac{243}{800}}{5^{-7}\times 6^{-3}}$$

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

$$\frac{\frac{243}{800}}{\frac{1}{78125}\times 6^{-3}}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\frac{\frac{243}{800}}{\frac{1}{78125}\times \frac{1}{216}}$$

Multiply \frac{1}{78125} and \frac{1}{216} to get \frac{1}{16875000}.

$$\frac{\frac{243}{800}}{\frac{1}{16875000}}$$

Divide \frac{243}{800} by \frac{1}{16875000} by multiplying \frac{243}{800} by the reciprocal of \frac{1}{16875000}.

$$\frac{243}{800}\times 16875000$$

Multiply \frac{243}{800} and 16875000 to get \frac{20503125}{4}.

$$\frac{20503125}{4}$$

Factor

$$\frac{3 ^ {8} \cdot 5 ^ {5}}{2 ^ {2}} = 5125781\frac{1}{4} = 5125781.25$$