Solve (a^3)^7/(b^4)^5

$$\frac { ( a ^ { 3 } ) ^ { 7 } } { ( b ^ { 4 } ) ^ { 5 } }$$

Evaluate

$$\frac{a^{21}}{b^{20}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 7 to get 21.

$$\frac{a^{21}}{\left(b^{4}\right)^{5}}$$

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

$$\frac{a^{21}}{b^{20}}$$

Differentiate w.r.t. a

$$21\times \left(\frac{a}{b}\right)^{20}$$