Solve left(x^2xright)^3^2

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

Evaluate

$$x^{27}$$

Steps for Raising Power to Another Power

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Calculate 3 to the power of 2 and get 9.

$$\left(x^{3}\right)^{9}$$

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

$$x^{3\times 9}$$

Multiply 3 times 9.

$$x^{27}$$

Differentiate w.r.t. x

$$27x^{26}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{3}\right)^{3^{2}})$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{3}\right)^{9})$$

To raise a power to another power, multiply the exponents. Multiply 3 and 9 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{27})$$

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

$$27x^{27-1}$$

Subtract 1 from 27.

$$27x^{26}$$