Solve frac{(x^{2})^{3}*y(y^3)^2}{x^4y^8}

$$\frac { ( x ^ { 2 } ) ^ { 3 } \cdot y ( y ^ { 3 } ) ^ { 2 } } { x ^ { 4 } y ^ { 8 } }$$

Evaluate

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

Solution Steps

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

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

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

$$\frac{x^{6}yy^{6}}{x^{4}y^{8}}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{x^{6}y^{7}}{x^{4}y^{8}}$$

Cancel out x^{4}y^{7} in both numerator and denominator.

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

Differentiate w.r.t. x

$$\frac{2x}{y}$$