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

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

Evaluate

$$\frac{2}{y^{9}}$$

Solution Steps

Calculate x to the power of 0 and get 1.

$$\frac{2\times 1y^{3}}{\left(x^{0}y^{3}\right)^{4}}$$

Multiply 2 and 1 to get 2.

$$\frac{2y^{3}}{\left(x^{0}y^{3}\right)^{4}}$$

Calculate x to the power of 0 and get 1.

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

Expand \left(1y^{3}\right)^{4}.

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

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

$$\frac{2y^{3}}{1^{4}y^{12}}$$

Calculate 1 to the power of 4 and get 1.

$$\frac{2y^{3}}{1y^{12}}$$

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

$$\frac{2}{y^{9}}$$

Differentiate w.r.t. y

$$-\frac{18}{y^{10}}$$