Solve (x^5)^3*(x^4)^2

$$( x ^ { 5 } ) ^ { 3 } \cdot ( x ^ { 4 } ) ^ { 2 }$$

Evaluate

$$x^{23}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(x^{5}\right)^{3}\left(x^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$x^{5\times 3}x^{4\times 2}$$

Multiply 5 times 3.

$$x^{15}x^{4\times 2}$$

Multiply 4 times 2.

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

To multiply powers of the same base, add their exponents.

$$x^{15+8}$$

Add the exponents 15 and 8.

$$x^{23}$$

Differentiate w.r.t. x

$$23x^{22}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{15}\left(x^{4}\right)^{2})$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{15}x^{8})$$

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

$$23x^{22}$$