Solve (x^2)(x^7)^3

$$( x ^ { 2 } ) ( x ^ { 7 } ) ^ { 3 }$$

Evaluate

$$x^{23}$$

Solution Steps

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

$$x^{2}x^{21}$$

To multiply powers of the same base, add their exponents. Add 2 and 21 to get 23.

$$x^{23}$$

Differentiate w.r.t. x

$$23x^{22}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x^{21})$$

To multiply powers of the same base, add their exponents. Add 2 and 21 to get 23.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{23})$$

The derivative of ax^{n} is nax^{n-1}.

$$23x^{23-1}$$

Subtract 1 from 23.

$$23x^{22}$$