Evaluate: /((2 y x ^-3) ^ 3) x ^ 0 y ^ 2*2 x ^ 3 y ^ 3

Expression: $$\frac { ( 2 y x ^ { - 3 } ) ^ { 3 } } { x ^ { 0 } y ^ { 2 } \cdot 2 x ^ { 3 } y ^ { 3 } }$$

To multiply powers of the same base, add their exponents. Add $0$ and $3$ to get $3$.

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

To multiply powers of the same base, add their exponents. Add $2$ and $3$ to get $5$.

$$\frac{\left(2yx^{-3}\right)^{3}}{x^{3}y^{5}\times 2}$$

Expand $\left(2yx^{-3}\right)^{3}$.

$$\frac{2^{3}y^{3}\left(x^{-3}\right)^{3}}{x^{3}y^{5}\times 2}$$

To raise a power to another power, multiply the exponents. Multiply $-3$ and $3$ to get $-9$.

$$\frac{2^{3}y^{3}x^{-9}}{x^{3}y^{5}\times 2}$$

Calculate $2$ to the power of $3$ and get $8$.

$$\frac{8y^{3}x^{-9}}{x^{3}y^{5}\times 2}$$

Cancel out $2y^{3}$ in both numerator and denominator.

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

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

$$\frac{4}{y^{2}x^{12}}$$