Solve frac{9^{-2}*10^-3*300}{3^-5*5^-6*2^-6}

$$\frac { 9 ^ { - 2 } \times 10 ^ { - 3 } \times 300 } { 3 ^ { - 5 } \times 5 ^ { - 6 } \times 2 ^ { - 6 } }$$

Evaluate

$$900000$$

Solution Steps

Calculate 9 to the power of -2 and get \frac{1}{81}.

$$\frac{\frac{1}{81}\times 10^{-3}\times 300}{3^{-5}\times 5^{-6}\times 2^{-6}}$$

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

$$\frac{\frac{1}{81}\times \frac{1}{1000}\times 300}{3^{-5}\times 5^{-6}\times 2^{-6}}$$

Multiply \frac{1}{81} and \frac{1}{1000} to get \frac{1}{81000}.

$$\frac{\frac{1}{81000}\times 300}{3^{-5}\times 5^{-6}\times 2^{-6}}$$

Multiply \frac{1}{81000} and 300 to get \frac{1}{270}.

$$\frac{\frac{1}{270}}{3^{-5}\times 5^{-6}\times 2^{-6}}$$

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

$$\frac{\frac{1}{270}}{\frac{1}{243}\times 5^{-6}\times 2^{-6}}$$

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

$$\frac{\frac{1}{270}}{\frac{1}{243}\times \frac{1}{15625}\times 2^{-6}}$$

Multiply \frac{1}{243} and \frac{1}{15625} to get \frac{1}{3796875}.

$$\frac{\frac{1}{270}}{\frac{1}{3796875}\times 2^{-6}}$$

Calculate 2 to the power of -6 and get \frac{1}{64}.

$$\frac{\frac{1}{270}}{\frac{1}{3796875}\times \frac{1}{64}}$$

Multiply \frac{1}{3796875} and \frac{1}{64} to get \frac{1}{243000000}.

$$\frac{\frac{1}{270}}{\frac{1}{243000000}}$$

Divide \frac{1}{270} by \frac{1}{243000000} by multiplying \frac{1}{270} by the reciprocal of \frac{1}{243000000}.

$$\frac{1}{270}\times 243000000$$

Multiply \frac{1}{270} and 243000000 to get 900000.

$$900000$$

Factor

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