Solve (((eta)^7)^7)^7)^7

$$( ( ( \eta ) ^ { 7 } ) ^ { 7 } ) ^ { 7 } ) ^ { 7 }$$

Evaluate

$$\eta ^{343}$$

Steps for Raising Power to Another Power

To raise a power to another power, multiply the exponents. Multiply 7 and 7 to get 49.

$$\left(\eta ^{49}\right)^{7}$$

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

$$\eta ^{49\times 7}$$

Multiply 49 times 7.

$$\eta ^{343}$$

Differentiate w.r.t. η

$$343\eta ^{342}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 7 and 7 to get 49.

$$\frac{\mathrm{d}}{\mathrm{d}\eta }(\left(\eta ^{49}\right)^{7})$$

To raise a power to another power, multiply the exponents. Multiply 49 and 7 to get 343.

$$\frac{\mathrm{d}}{\mathrm{d}\eta }(\eta ^{343})$$

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

$$343\eta ^{343-1}$$

Subtract 1 from 343.

$$343\eta ^{342}$$