Solve frac{(u^{4})^{3}*(a^{5})^{2}}{(u^3)^4*(u^2)^3}

$$\frac { ( u ^ { 4 } ) ^ { 3 } \times ( a ^ { 5 } ) ^ { 2 } } { ( u ^ { 3 } ) ^ { 4 } \times ( u ^ { 2 } ) ^ { 3 } }$$

Evaluate

$$\frac{a^{10}}{u^{6}}$$

Solution Steps

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

$$\frac{u^{12}\left(a^{5}\right)^{2}}{\left(u^{3}\right)^{4}\left(u^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{u^{12}a^{10}}{\left(u^{3}\right)^{4}\left(u^{2}\right)^{3}}$$

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

$$\frac{u^{12}a^{10}}{u^{12}\left(u^{2}\right)^{3}}$$

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

$$\frac{u^{12}a^{10}}{u^{12}u^{6}}$$

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$\frac{u^{12}a^{10}}{u^{18}}$$

Cancel out u^{12} in both numerator and denominator.

$$\frac{a^{10}}{u^{6}}$$

Differentiate w.r.t. a

$$\frac{10a^{9}}{u^{6}}$$