Solve (-x^{4}y^{2})^3-(-2/3x^6y^3)^2

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

Evaluate

$$-\frac{13y^{6}x^{12}}{9}$$

Solution Steps

Expand \left(\left(-x^{4}\right)y^{2}\right)^{3}.

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

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

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

Expand \left(-\frac{2}{3}x^{6}y^{3}\right)^{2}.

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

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

$$\left(-x^{4}\right)^{3}y^{6}-\left(-\frac{2}{3}\right)^{2}x^{12}\left(y^{3}\right)^{2}$$

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

$$\left(-x^{4}\right)^{3}y^{6}-\left(-\frac{2}{3}\right)^{2}x^{12}y^{6}$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\left(-x^{4}\right)^{3}y^{6}-\frac{4}{9}x^{12}y^{6}$$

Expand \left(-x^{4}\right)^{3}.

$$\left(-1\right)^{3}\left(x^{4}\right)^{3}y^{6}-\frac{4}{9}x^{12}y^{6}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(-1\right)^{3}x^{12}y^{6}-\frac{4}{9}x^{12}y^{6}$$

Calculate -1 to the power of 3 and get -1.

$$-x^{12}y^{6}-\frac{4}{9}x^{12}y^{6}$$

Combine -x^{12}y^{6} and -\frac{4}{9}x^{12}y^{6} to get -\frac{13}{9}x^{12}y^{6}.

$$-\frac{13}{9}x^{12}y^{6}$$

Expand

$$-\frac{13y^{6}x^{12}}{9}$$

Solution Steps

Expand \left(\left(-x^{4}\right)y^{2}\right)^{3}.

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

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

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

Expand \left(-\frac{2}{3}x^{6}y^{3}\right)^{2}.

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

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

$$\left(-x^{4}\right)^{3}y^{6}-\left(-\frac{2}{3}\right)^{2}x^{12}\left(y^{3}\right)^{2}$$

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

$$\left(-x^{4}\right)^{3}y^{6}-\left(-\frac{2}{3}\right)^{2}x^{12}y^{6}$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\left(-x^{4}\right)^{3}y^{6}-\frac{4}{9}x^{12}y^{6}$$

Expand \left(-x^{4}\right)^{3}.

$$\left(-1\right)^{3}\left(x^{4}\right)^{3}y^{6}-\frac{4}{9}x^{12}y^{6}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(-1\right)^{3}x^{12}y^{6}-\frac{4}{9}x^{12}y^{6}$$

Calculate -1 to the power of 3 and get -1.

$$-x^{12}y^{6}-\frac{4}{9}x^{12}y^{6}$$

Combine -x^{12}y^{6} and -\frac{4}{9}x^{12}y^{6} to get -\frac{13}{9}x^{12}y^{6}.

$$-\frac{13}{9}x^{12}y^{6}$$