Solve (-1/3x^{4}y^2)^3+(-2x^2y)^6

$$( - \frac { 1 } { 3 } x ^ { 4 } y ^ { 2 } ) ^ { 3 } + ( - 2 x ^ { 2 } y ) ^ { 6 }$$

Evaluate

$$\frac{1727y^{6}x^{12}}{27}$$

Solution Steps

Expand \left(-\frac{1}{3}x^{4}y^{2}\right)^{3}.

$$\left(-\frac{1}{3}\right)^{3}\left(x^{4}\right)^{3}\left(y^{2}\right)^{3}+\left(-2x^{2}y\right)^{6}$$

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

$$\left(-\frac{1}{3}\right)^{3}x^{12}\left(y^{2}\right)^{3}+\left(-2x^{2}y\right)^{6}$$

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

$$\left(-\frac{1}{3}\right)^{3}x^{12}y^{6}+\left(-2x^{2}y\right)^{6}$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$-\frac{1}{27}x^{12}y^{6}+\left(-2x^{2}y\right)^{6}$$

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

$$-\frac{1}{27}x^{12}y^{6}+\left(-2\right)^{6}\left(x^{2}\right)^{6}y^{6}$$

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

$$-\frac{1}{27}x^{12}y^{6}+\left(-2\right)^{6}x^{12}y^{6}$$

Calculate -2 to the power of 6 and get 64.

$$-\frac{1}{27}x^{12}y^{6}+64x^{12}y^{6}$$

Combine -\frac{1}{27}x^{12}y^{6} and 64x^{12}y^{6} to get \frac{1727}{27}x^{12}y^{6}.

$$\frac{1727}{27}x^{12}y^{6}$$

Expand

$$\frac{1727y^{6}x^{12}}{27}$$

Solution Steps

Expand \left(-\frac{1}{3}x^{4}y^{2}\right)^{3}.

$$\left(-\frac{1}{3}\right)^{3}\left(x^{4}\right)^{3}\left(y^{2}\right)^{3}+\left(-2x^{2}y\right)^{6}$$

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

$$\left(-\frac{1}{3}\right)^{3}x^{12}\left(y^{2}\right)^{3}+\left(-2x^{2}y\right)^{6}$$

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

$$\left(-\frac{1}{3}\right)^{3}x^{12}y^{6}+\left(-2x^{2}y\right)^{6}$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$-\frac{1}{27}x^{12}y^{6}+\left(-2x^{2}y\right)^{6}$$

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

$$-\frac{1}{27}x^{12}y^{6}+\left(-2\right)^{6}\left(x^{2}\right)^{6}y^{6}$$

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

$$-\frac{1}{27}x^{12}y^{6}+\left(-2\right)^{6}x^{12}y^{6}$$

Calculate -2 to the power of 6 and get 64.

$$-\frac{1}{27}x^{12}y^{6}+64x^{12}y^{6}$$

Combine -\frac{1}{27}x^{12}y^{6} and 64x^{12}y^{6} to get \frac{1727}{27}x^{12}y^{6}.

$$\frac{1727}{27}x^{12}y^{6}$$