Solve 6^-22^-2/5^-23^2

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

Evaluate

$$\frac{25}{1296}\approx 0.019290123$$

Solution Steps

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{\frac{1}{36}\times 2^{-2}}{5^{-2}\times 3^{2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{36}\times \frac{1}{4}}{5^{-2}\times 3^{2}}$$

Multiply \frac{1}{36} and \frac{1}{4} to get \frac{1}{144}.

$$\frac{\frac{1}{144}}{5^{-2}\times 3^{2}}$$

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

$$\frac{\frac{1}{144}}{\frac{1}{25}\times 3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{1}{144}}{\frac{1}{25}\times 9}$$

Multiply \frac{1}{25} and 9 to get \frac{9}{25}.

$$\frac{\frac{1}{144}}{\frac{9}{25}}$$

Divide \frac{1}{144} by \frac{9}{25} by multiplying \frac{1}{144} by the reciprocal of \frac{9}{25}.

$$\frac{1}{144}\times \frac{25}{9}$$

Multiply \frac{1}{144} and \frac{25}{9} to get \frac{25}{1296}.

$$\frac{25}{1296}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {4} \cdot 3 ^ {4}} = 0.019290123456790122$$