Solve frac{(3x^{-1}y^-2)^-2}{(3xy^2)^2}=

$$\frac { ( 3 x ^ { - 1 } y ^ { - 2 } ) ^ { - 2 } } { ( 3 x y ^ { 2 } ) ^ { 2 } } =$$

Evaluate

$$\frac{1}{81}\approx 0.012345679$$

Solution Steps

Expand \left(3x^{-1}y^{-2}\right)^{-2}.

$$\frac{3^{-2}\left(x^{-1}\right)^{-2}\left(y^{-2}\right)^{-2}}{\left(3xy^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\frac{3^{-2}x^{2}\left(y^{-2}\right)^{-2}}{\left(3xy^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -2 to get 4.

$$\frac{3^{-2}x^{2}y^{4}}{\left(3xy^{2}\right)^{2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}x^{2}y^{4}}{\left(3xy^{2}\right)^{2}}$$

Expand \left(3xy^{2}\right)^{2}.

$$\frac{\frac{1}{9}x^{2}y^{4}}{3^{2}x^{2}\left(y^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\frac{1}{9}x^{2}y^{4}}{3^{2}x^{2}y^{4}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{1}{9}x^{2}y^{4}}{9x^{2}y^{4}}$$

Cancel out x^{2}y^{4} in both numerator and denominator.

$$\frac{\frac{1}{9}}{9}$$

Express \frac{\frac{1}{9}}{9} as a single fraction.

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

Multiply 9 and 9 to get 81.

$$\frac{1}{81}$$

Factor

$$\frac{1}{3 ^ {4}} = 0.012345679012345678$$