Solve {left(x^2right)}^left(2^2right)^left(2^2right)^2

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

Evaluate

$$x^{8589934592}$$

Steps for Raising Power to Another Power

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

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 2 to the power of 4 and get 16.

$$\left(x^{2}\right)^{4^{16}}$$

Calculate 4 to the power of 16 and get 4294967296.

$$\left(x^{2}\right)^{4294967296}$$

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

$$x^{2\times 4294967296}$$

Multiply 2 times 4294967296.

$$x^{8589934592}$$

Differentiate w.r.t. x

$$8589934592x^{8589934591}$$

Steps Using Definition of a Derivative

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

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{2}\right)^{4^{16}})$$

Calculate 4 to the power of 16 and get 4294967296.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{2}\right)^{4294967296})$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4294967296 to get 8589934592.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8589934592})$$

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

$$8589934592x^{8589934592-1}$$

Subtract 1 from 8589934592.

$$8589934592x^{8589934591}$$