Solve (-2x^{5}y^{3})^{4}div(-x^{4}y^3)^2divx^3y^2

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

Evaluate

$$16y^{8}x^{9}$$

Solution Steps

Express \frac{\frac{\left(-2x^{5}y^{3}\right)^{4}}{\left(\left(-x^{4}\right)y^{3}\right)^{2}}}{x^{3}} as a single fraction.

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

Expand \left(-2x^{5}y^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{\left(-2\right)^{4}x^{20}\left(y^{3}\right)^{4}}{\left(\left(-x^{4}\right)y^{3}\right)^{2}x^{3}}y^{2}$$

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

$$\frac{\left(-2\right)^{4}x^{20}y^{12}}{\left(\left(-x^{4}\right)y^{3}\right)^{2}x^{3}}y^{2}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{16x^{20}y^{12}}{\left(\left(-x^{4}\right)y^{3}\right)^{2}x^{3}}y^{2}$$

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

$$\frac{16x^{20}y^{12}}{\left(-x^{4}\right)^{2}\left(y^{3}\right)^{2}x^{3}}y^{2}$$

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

$$\frac{16x^{20}y^{12}}{\left(-x^{4}\right)^{2}y^{6}x^{3}}y^{2}$$

Calculate -x^{4} to the power of 2 and get \left(x^{4}\right)^{2}.

$$\frac{16x^{20}y^{12}}{\left(x^{4}\right)^{2}y^{6}x^{3}}y^{2}$$

Cancel out x^{3}y^{6} in both numerator and denominator.

$$\frac{16y^{6}x^{17}}{\left(x^{4}\right)^{2}}y^{2}$$

Express \frac{16y^{6}x^{17}}{\left(x^{4}\right)^{2}}y^{2} as a single fraction.

$$\frac{16y^{6}x^{17}y^{2}}{\left(x^{4}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{16y^{8}x^{17}}{\left(x^{4}\right)^{2}}$$

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

$$\frac{16y^{8}x^{17}}{x^{8}}$$

Cancel out x^{8} in both numerator and denominator.

$$16y^{8}x^{9}$$

Expand

$$16y^{8}x^{9}$$

Solution Steps

Express \frac{\frac{\left(-2x^{5}y^{3}\right)^{4}}{\left(\left(-x^{4}\right)y^{3}\right)^{2}}}{x^{3}} as a single fraction.

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

Expand \left(-2x^{5}y^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{\left(-2\right)^{4}x^{20}\left(y^{3}\right)^{4}}{\left(\left(-x^{4}\right)y^{3}\right)^{2}x^{3}}y^{2}$$

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

$$\frac{\left(-2\right)^{4}x^{20}y^{12}}{\left(\left(-x^{4}\right)y^{3}\right)^{2}x^{3}}y^{2}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{16x^{20}y^{12}}{\left(\left(-x^{4}\right)y^{3}\right)^{2}x^{3}}y^{2}$$

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

$$\frac{16x^{20}y^{12}}{\left(-x^{4}\right)^{2}\left(y^{3}\right)^{2}x^{3}}y^{2}$$

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

$$\frac{16x^{20}y^{12}}{\left(-x^{4}\right)^{2}y^{6}x^{3}}y^{2}$$

Calculate -x^{4} to the power of 2 and get \left(x^{4}\right)^{2}.

$$\frac{16x^{20}y^{12}}{\left(x^{4}\right)^{2}y^{6}x^{3}}y^{2}$$

Cancel out x^{3}y^{6} in both numerator and denominator.

$$\frac{16y^{6}x^{17}}{\left(x^{4}\right)^{2}}y^{2}$$

Express \frac{16y^{6}x^{17}}{\left(x^{4}\right)^{2}}y^{2} as a single fraction.

$$\frac{16y^{6}x^{17}y^{2}}{\left(x^{4}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{16y^{8}x^{17}}{\left(x^{4}\right)^{2}}$$

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

$$\frac{16y^{8}x^{17}}{x^{8}}$$

Cancel out x^{8} in both numerator and denominator.

$$16y^{8}x^{9}$$