Solve (-xy^{2})^3+1/5xy^4(10/3x^2y^2)

$$( - x y ^ { 2 } ) ^ { 3 } + \frac { 1 } { 5 } x y ^ { 4 } ( \frac { 10 } { 3 } x ^ { 2 } y ^ { 2 } )$$

Evaluate

$$-\frac{x^{3}y^{6}}{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(\left(-x\right)y^{2}\right)^{3}+\frac{1}{5}x^{3}y^{4}\times \frac{10}{3}y^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\left(\left(-x\right)y^{2}\right)^{3}+\frac{1}{5}x^{3}y^{6}\times \frac{10}{3}$$

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

$$\left(-x\right)^{3}\left(y^{2}\right)^{3}+\frac{1}{5}x^{3}y^{6}\times \frac{10}{3}$$

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

$$\left(-x\right)^{3}y^{6}+\frac{1}{5}x^{3}y^{6}\times \frac{10}{3}$$

Multiply \frac{1}{5} and \frac{10}{3} to get \frac{2}{3}.

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

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

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

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

$$-x^{3}y^{6}+\frac{2}{3}x^{3}y^{6}$$

Combine -x^{3}y^{6} and \frac{2}{3}x^{3}y^{6} to get -\frac{1}{3}x^{3}y^{6}.

$$-\frac{1}{3}x^{3}y^{6}$$

Expand

$$-\frac{x^{3}y^{6}}{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(\left(-x\right)y^{2}\right)^{3}+\frac{1}{5}x^{3}y^{4}\times \frac{10}{3}y^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\left(\left(-x\right)y^{2}\right)^{3}+\frac{1}{5}x^{3}y^{6}\times \frac{10}{3}$$

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

$$\left(-x\right)^{3}\left(y^{2}\right)^{3}+\frac{1}{5}x^{3}y^{6}\times \frac{10}{3}$$

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

$$\left(-x\right)^{3}y^{6}+\frac{1}{5}x^{3}y^{6}\times \frac{10}{3}$$

Multiply \frac{1}{5} and \frac{10}{3} to get \frac{2}{3}.

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

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

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

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

$$-x^{3}y^{6}+\frac{2}{3}x^{3}y^{6}$$

Combine -x^{3}y^{6} and \frac{2}{3}x^{3}y^{6} to get -\frac{1}{3}x^{3}y^{6}.

$$-\frac{1}{3}x^{3}y^{6}$$