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

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

Evaluate

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

Solution Steps

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

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

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

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

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

$$\frac{x^{8}y^{12}}{\left(\left(-x^{2}\right)y^{3}\right)^{2}}\left(x^{2}y^{3}\right)^{2}$$

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

$$\frac{x^{8}y^{12}}{\left(-x^{2}\right)^{2}\left(y^{3}\right)^{2}}\left(x^{2}y^{3}\right)^{2}$$

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

$$\frac{x^{8}y^{12}}{\left(-x^{2}\right)^{2}y^{6}}\left(x^{2}y^{3}\right)^{2}$$

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

$$\frac{x^{8}y^{12}}{\left(x^{2}\right)^{2}y^{6}}\left(x^{2}y^{3}\right)^{2}$$

Cancel out y^{6} in both numerator and denominator.

$$\frac{y^{6}x^{8}}{\left(x^{2}\right)^{2}}\left(x^{2}y^{3}\right)^{2}$$

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

$$\frac{y^{6}x^{8}}{\left(x^{2}\right)^{2}}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}$$

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

$$\frac{y^{6}x^{8}}{\left(x^{2}\right)^{2}}x^{4}\left(y^{3}\right)^{2}$$

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

$$\frac{y^{6}x^{8}}{\left(x^{2}\right)^{2}}x^{4}y^{6}$$

Express \frac{y^{6}x^{8}}{\left(x^{2}\right)^{2}}x^{4} as a single fraction.

$$\frac{y^{6}x^{8}x^{4}}{\left(x^{2}\right)^{2}}y^{6}$$

Express \frac{y^{6}x^{8}x^{4}}{\left(x^{2}\right)^{2}}y^{6} as a single fraction.

$$\frac{y^{6}x^{8}x^{4}y^{6}}{\left(x^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

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

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

$$\frac{y^{12}x^{12}}{\left(x^{2}\right)^{2}}$$

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

$$\frac{y^{12}x^{12}}{x^{4}}$$

Cancel out x^{4} in both numerator and denominator.

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

Expand

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

Solution Steps

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

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

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

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

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

$$\frac{x^{8}y^{12}}{\left(\left(-x^{2}\right)y^{3}\right)^{2}}\left(x^{2}y^{3}\right)^{2}$$

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

$$\frac{x^{8}y^{12}}{\left(-x^{2}\right)^{2}\left(y^{3}\right)^{2}}\left(x^{2}y^{3}\right)^{2}$$

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

$$\frac{x^{8}y^{12}}{\left(-x^{2}\right)^{2}y^{6}}\left(x^{2}y^{3}\right)^{2}$$

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

$$\frac{x^{8}y^{12}}{\left(x^{2}\right)^{2}y^{6}}\left(x^{2}y^{3}\right)^{2}$$

Cancel out y^{6} in both numerator and denominator.

$$\frac{y^{6}x^{8}}{\left(x^{2}\right)^{2}}\left(x^{2}y^{3}\right)^{2}$$

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

$$\frac{y^{6}x^{8}}{\left(x^{2}\right)^{2}}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}$$

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

$$\frac{y^{6}x^{8}}{\left(x^{2}\right)^{2}}x^{4}\left(y^{3}\right)^{2}$$

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

$$\frac{y^{6}x^{8}}{\left(x^{2}\right)^{2}}x^{4}y^{6}$$

Express \frac{y^{6}x^{8}}{\left(x^{2}\right)^{2}}x^{4} as a single fraction.

$$\frac{y^{6}x^{8}x^{4}}{\left(x^{2}\right)^{2}}y^{6}$$

Express \frac{y^{6}x^{8}x^{4}}{\left(x^{2}\right)^{2}}y^{6} as a single fraction.

$$\frac{y^{6}x^{8}x^{4}y^{6}}{\left(x^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

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

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

$$\frac{y^{12}x^{12}}{\left(x^{2}\right)^{2}}$$

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

$$\frac{y^{12}x^{12}}{x^{4}}$$

Cancel out x^{4} in both numerator and denominator.

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