Solve {left(left(3xyright)^3/2right)}^2

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

Evaluate

$$\frac{729\left(xy\right)^{6}}{4}$$

Solution Steps

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

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

Calculate 3 to the power of 3 and get 27.

$$\left(\frac{27x^{3}y^{3}}{2}\right)^{2}$$

To raise \frac{27x^{3}y^{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(27x^{3}y^{3}\right)^{2}}{2^{2}}$$

Expand \left(27x^{3}y^{3}\right)^{2}.

$$\frac{27^{2}\left(x^{3}\right)^{2}\left(y^{3}\right)^{2}}{2^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{27^{2}x^{6}\left(y^{3}\right)^{2}}{2^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{27^{2}x^{6}y^{6}}{2^{2}}$$

Calculate 27 to the power of 2 and get 729.

$$\frac{729x^{6}y^{6}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{729x^{6}y^{6}}{4}$$

Expand

$$\frac{729\left(xy\right)^{6}}{4}$$

Solution Steps

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

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

Calculate 3 to the power of 3 and get 27.

$$\left(\frac{27x^{3}y^{3}}{2}\right)^{2}$$

To raise \frac{27x^{3}y^{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(27x^{3}y^{3}\right)^{2}}{2^{2}}$$

Expand \left(27x^{3}y^{3}\right)^{2}.

$$\frac{27^{2}\left(x^{3}\right)^{2}\left(y^{3}\right)^{2}}{2^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{27^{2}x^{6}\left(y^{3}\right)^{2}}{2^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{27^{2}x^{6}y^{6}}{2^{2}}$$

Calculate 27 to the power of 2 and get 729.

$$\frac{729x^{6}y^{6}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{729x^{6}y^{6}}{4}$$