Solve (3x^3/2y)^2

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

Evaluate

$$\frac{9x^{6}}{4y^{2}}$$

Solution Steps

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

$$\frac{9x^{6}}{2^{2}y^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{9x^{6}}{4y^{2}}$$

Expand

$$\frac{9x^{6}}{4y^{2}}$$

Solution Steps

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

$$\frac{9x^{6}}{2^{2}y^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{9x^{6}}{4y^{2}}$$