Solve frac{3^{-5}*10^-5*125^9}{5^-6*6^-5}

$$\frac { 3 ^ { - 5 } \times 10 ^ { - 5 } \times 125 ^ { 9 } } { 5 ^ { - 6 } \times 6 ^ { - 5 } }$$

Evaluate

$$37252902984619140625$$

Solution Steps

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

$$\frac{\frac{1}{243}\times 10^{-5}\times 125^{9}}{5^{-6}\times 6^{-5}}$$

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

$$\frac{\frac{1}{243}\times \frac{1}{100000}\times 125^{9}}{5^{-6}\times 6^{-5}}$$

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

$$\frac{\frac{1}{24300000}\times 125^{9}}{5^{-6}\times 6^{-5}}$$

Calculate 125 to the power of 9 and get 7450580596923828125.

$$\frac{\frac{1}{24300000}\times 7450580596923828125}{5^{-6}\times 6^{-5}}$$

Multiply \frac{1}{24300000} and 7450580596923828125 to get \frac{2384185791015625}{7776}.

$$\frac{\frac{2384185791015625}{7776}}{5^{-6}\times 6^{-5}}$$

Calculate 5 to the power of -6 and get \frac{1}{15625}.

$$\frac{\frac{2384185791015625}{7776}}{\frac{1}{15625}\times 6^{-5}}$$

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

$$\frac{\frac{2384185791015625}{7776}}{\frac{1}{15625}\times \frac{1}{7776}}$$

Multiply \frac{1}{15625} and \frac{1}{7776} to get \frac{1}{121500000}.

$$\frac{\frac{2384185791015625}{7776}}{\frac{1}{121500000}}$$

Divide \frac{2384185791015625}{7776} by \frac{1}{121500000} by multiplying \frac{2384185791015625}{7776} by the reciprocal of \frac{1}{121500000}.

$$\frac{2384185791015625}{7776}\times 121500000$$

Multiply \frac{2384185791015625}{7776} and 121500000 to get 37252902984619140625.

$$37252902984619140625$$

Factor

$$5^{28}$$