Solve (x^{2}y^{3})^{0}(x^{4}y^3)^4/(xy^2)^3

$$( x ^ { 2 } y ^ { 3 } ) ^ { 0 } ( x ^ { 4 } y ^ { 3 } ) ^ { 4 } / ( x y ^ { 2 } ) ^ { 3 }$$

Evaluate

$$y^{6}x^{13}$$

Solution Steps

Calculate x^{2}y^{3} to the power of 0 and get 1.

$$\frac{1\left(x^{4}y^{3}\right)^{4}}{\left(xy^{2}\right)^{3}}$$

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

$$\frac{1\left(x^{4}\right)^{4}\left(y^{3}\right)^{4}}{\left(xy^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{1x^{16}\left(y^{3}\right)^{4}}{\left(xy^{2}\right)^{3}}$$

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

$$\frac{1x^{16}y^{12}}{\left(xy^{2}\right)^{3}}$$

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

$$\frac{1x^{16}y^{12}}{x^{3}\left(y^{2}\right)^{3}}$$

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

$$\frac{1x^{16}y^{12}}{x^{3}y^{6}}$$

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

$$y^{6}x^{13}$$

Differentiate w.r.t. x

$$13y^{6}x^{12}$$