Solve ax(x^3)^2x(x^5)^3

$$a x ( x ^ { 3 } ) ^ { 2 } x ( x ^ { 5 } ) ^ { 3 }$$

Evaluate

$$ax^{23}$$

Solution Steps

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

$$axx^{6}x\left(x^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$axx^{6}xx^{15}$$

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

$$ax^{7}xx^{15}$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$ax^{8}x^{15}$$

To multiply powers of the same base, add their exponents. Add 8 and 15 to get 23.

$$ax^{23}$$

Differentiate w.r.t. x

$$23ax^{22}$$