Solve -xy^{2}*(-2x^{2}y)^{3}+x^{4}*5x^{3}y^{5}-3x^3y*(-x^2y^2)^2

$$- x y ^ { 2 } \cdot ( - 2 x ^ { 2 } y ) ^ { 3 } + x ^ { 4 } \cdot 5 x ^ { 3 } y ^ { 5 } - 3 x ^ { 3 } y \cdot ( - x ^ { 2 } y ^ { 2 } ) ^ { 2 }$$

Evaluate

$$10y^{5}x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\left(-x\right)y^{2}\left(-2x^{2}y\right)^{3}+x^{7}\times 5y^{5}-3x^{3}y\left(\left(-x^{2}\right)y^{2}\right)^{2}$$

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

$$\left(-x\right)y^{2}\left(-2\right)^{3}\left(x^{2}\right)^{3}y^{3}+x^{7}\times 5y^{5}-3x^{3}y\left(\left(-x^{2}\right)y^{2}\right)^{2}$$

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

$$\left(-x\right)y^{2}\left(-2\right)^{3}x^{6}y^{3}+x^{7}\times 5y^{5}-3x^{3}y\left(\left(-x^{2}\right)y^{2}\right)^{2}$$

Calculate -2 to the power of 3 and get -8.

$$\left(-x\right)y^{2}\left(-8\right)x^{6}y^{3}+x^{7}\times 5y^{5}-3x^{3}y\left(\left(-x^{2}\right)y^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y\left(\left(-x^{2}\right)y^{2}\right)^{2}$$

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

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y\left(-x^{2}\right)^{2}\left(y^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y\left(-x^{2}\right)^{2}y^{4}$$

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y\left(x^{2}\right)^{2}y^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y^{5}\left(x^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y^{5}x^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{7}y^{5}$$

Combine x^{7}\times 5y^{5} and -3x^{7}y^{5} to get 2x^{7}y^{5}.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+2x^{7}y^{5}$$

Multiply -1 and -8 to get 8.

$$8xy^{5}x^{6}+2x^{7}y^{5}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$8x^{7}y^{5}+2x^{7}y^{5}$$

Combine 8x^{7}y^{5} and 2x^{7}y^{5} to get 10x^{7}y^{5}.

$$10x^{7}y^{5}$$

Expand

$$10y^{5}x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\left(-x\right)y^{2}\left(-2x^{2}y\right)^{3}+x^{7}\times 5y^{5}-3x^{3}y\left(\left(-x^{2}\right)y^{2}\right)^{2}$$

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

$$\left(-x\right)y^{2}\left(-2\right)^{3}\left(x^{2}\right)^{3}y^{3}+x^{7}\times 5y^{5}-3x^{3}y\left(\left(-x^{2}\right)y^{2}\right)^{2}$$

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

$$\left(-x\right)y^{2}\left(-2\right)^{3}x^{6}y^{3}+x^{7}\times 5y^{5}-3x^{3}y\left(\left(-x^{2}\right)y^{2}\right)^{2}$$

Calculate -2 to the power of 3 and get -8.

$$\left(-x\right)y^{2}\left(-8\right)x^{6}y^{3}+x^{7}\times 5y^{5}-3x^{3}y\left(\left(-x^{2}\right)y^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y\left(\left(-x^{2}\right)y^{2}\right)^{2}$$

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

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y\left(-x^{2}\right)^{2}\left(y^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y\left(-x^{2}\right)^{2}y^{4}$$

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y\left(x^{2}\right)^{2}y^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y^{5}\left(x^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{3}y^{5}x^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+x^{7}\times 5y^{5}-3x^{7}y^{5}$$

Combine x^{7}\times 5y^{5} and -3x^{7}y^{5} to get 2x^{7}y^{5}.

$$\left(-x\right)y^{5}\left(-8\right)x^{6}+2x^{7}y^{5}$$

Multiply -1 and -8 to get 8.

$$8xy^{5}x^{6}+2x^{7}y^{5}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$8x^{7}y^{5}+2x^{7}y^{5}$$

Combine 8x^{7}y^{5} and 2x^{7}y^{5} to get 10x^{7}y^{5}.

$$10x^{7}y^{5}$$