Calculate: (/(3 x ^ 9) 4 y ^ 6) ^ 2

Expression: $$( \frac { 3 x ^ { 9 } } { 4 y ^ { 6 } } ) ^ { 2 }$$

To raise $\frac{3x^{9}}{4y^{6}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x^{9}\right)^{2}}{\left(4y^{6}\right)^{2}}$$

Expand $\left(3x^{9}\right)^{2}$.

$$\frac{3^{2}\left(x^{9}\right)^{2}}{\left(4y^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $9$ and $2$ to get $18$.

$$\frac{3^{2}x^{18}}{\left(4y^{6}\right)^{2}}$$

Calculate $3$ to the power of $2$ and get $9$.

$$\frac{9x^{18}}{\left(4y^{6}\right)^{2}}$$

Expand $\left(4y^{6}\right)^{2}$.

$$\frac{9x^{18}}{4^{2}\left(y^{6}\right)^{2}}$$

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

$$\frac{9x^{18}}{4^{2}y^{12}}$$

Calculate $4$ to the power of $2$ and get $16$.

$$\frac{9x^{18}}{16y^{12}}$$