Solve x^2left(x^2right)^22^22*545

$${ x }^{ 2 } { \left( { x }^{ 2 } \right) }^{ 2 { 2 }^{ 2 } 2 \times 545 }$$

Evaluate

$$x^{17442}$$

Solution Steps

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

$$x^{2}\left(x^{2}\right)^{2^{3}\times 2\times 545}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{2}\left(x^{2}\right)^{2^{4}\times 545}$$

Calculate 2 to the power of 4 and get 16.

$$x^{2}\left(x^{2}\right)^{16\times 545}$$

Multiply 16 and 545 to get 8720.

$$x^{2}\left(x^{2}\right)^{8720}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 8720 to get 17440.

$$x^{2}x^{17440}$$

To multiply powers of the same base, add their exponents. Add 2 and 17440 to get 17442.

$$x^{17442}$$

Differentiate w.r.t. x

$$17442x^{17441}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\left(x^{2}\right)^{2^{3}\times 2\times 545})$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\left(x^{2}\right)^{2^{4}\times 545})$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\left(x^{2}\right)^{16\times 545})$$

Multiply 16 and 545 to get 8720.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\left(x^{2}\right)^{8720})$$

To raise a power to another power, multiply the exponents. Multiply 2 and 8720 to get 17440.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x^{17440})$$

To multiply powers of the same base, add their exponents. Add 2 and 17440 to get 17442.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{17442})$$

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

$$17442x^{17442-1}$$

Subtract 1 from 17442.

$$17442x^{17441}$$