Solve 5^-2*6^-3*5^4/6^-6

$$5 ^ { - 2 } \cdot 6 ^ { - 3 } \cdot \frac { 5 ^ { 4 } } { 6 ^ { - 6 } }$$

Evaluate

$$5400$$

Solution Steps

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{1}{25}\times 6^{-3}\times \frac{5^{4}}{6^{-6}}$$

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

$$\frac{1}{25}\times \frac{1}{216}\times \frac{5^{4}}{6^{-6}}$$

Multiply \frac{1}{25} and \frac{1}{216} to get \frac{1}{5400}.

$$\frac{1}{5400}\times \frac{5^{4}}{6^{-6}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{1}{5400}\times \frac{625}{6^{-6}}$$

Calculate 6 to the power of -6 and get \frac{1}{46656}.

$$\frac{1}{5400}\times \frac{625}{\frac{1}{46656}}$$

Divide 625 by \frac{1}{46656} by multiplying 625 by the reciprocal of \frac{1}{46656}.

$$\frac{1}{5400}\times 625\times 46656$$

Multiply 625 and 46656 to get 29160000.

$$\frac{1}{5400}\times 29160000$$

Multiply \frac{1}{5400} and 29160000 to get 5400.

$$5400$$

Factor

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