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

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

Evaluate

$$x^{81}$$

Solution Steps

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

$$x^{3^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$x^{81}$$

Differentiate w.r.t. x

$$81x^{80}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3^{4}})$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{81})$$

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

$$81x^{81-1}$$

Subtract 1 from 81.

$$81x^{80}$$