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

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

Evaluate

$$0$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$x^{8}\left(y^{3}\right)^{4}-\left(x^{4}y^{4}\right)^{2}y^{4}$$

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

$$x^{8}y^{12}-\left(x^{4}y^{4}\right)^{2}y^{4}$$

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

$$x^{8}y^{12}-\left(x^{4}\right)^{2}\left(y^{4}\right)^{2}y^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{8}y^{12}-x^{8}\left(y^{4}\right)^{2}y^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{8}y^{12}-x^{8}y^{8}y^{4}$$

To multiply powers of the same base, add their exponents. Add 8 and 4 to get 12.

$$x^{8}y^{12}-x^{8}y^{12}$$

Combine x^{8}y^{12} and -x^{8}y^{12} to get 0.

$$0$$

Factor

$$0$$