Calculate: (/(2 x ^ 3 y ^-3) x ^-3 y ^ 4) ^-2

Expression: $$( \frac { 2 x ^ { 3 } y ^ { - 3 } } { x ^ { - 3 } y ^ { 4 } } ) ^ { - 2 }$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{2y^{-3}x^{6}}{y^{4}}\right)^{-2}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{2x^{6}}{y^{7}}\right)^{-2}$$

To raise $\frac{2x^{6}}{y^{7}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{6}\right)^{-2}}{\left(y^{7}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply $7$ and $-2$ to get $-14$.

$$\frac{\left(2x^{6}\right)^{-2}}{y^{-14}}$$

Expand $\left(2x^{6}\right)^{-2}$.

$$\frac{2^{-2}\left(x^{6}\right)^{-2}}{y^{-14}}$$

To raise a power to another power, multiply the exponents. Multiply $6$ and $-2$ to get $-12$.

$$\frac{2^{-2}x^{-12}}{y^{-14}}$$

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

$$\frac{\frac{1}{4}x^{-12}}{y^{-14}}$$