Solve (a^4)^6(b^5)^-2

$$( a ^ { 4 } ) ^ { 6 } ( b ^ { 5 } ) ^ { - 2 }$$

Evaluate

$$\frac{a^{24}}{b^{10}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.

$$a^{24}\left(b^{5}\right)^{-2}$$

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

$$a^{24}b^{-10}$$

Differentiate w.r.t. a

$$\frac{24a^{23}}{b^{10}}$$