Solve ((y^3)^3)^6

$$( ( y ^ { 3 } ) ^ { 3 } ) ^ { 6 }$$

Evaluate

$$y^{54}$$

Steps for Raising Power to Another Power

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

$$\left(y^{9}\right)^{6}$$

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

$$y^{9\times 6}$$

Multiply 9 times 6.

$$y^{54}$$

Differentiate w.r.t. y

$$54y^{53}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(y^{9}\right)^{6})$$

To raise a power to another power, multiply the exponents. Multiply 9 and 6 to get 54.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{54})$$

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

$$54y^{54-1}$$

Subtract 1 from 54.

$$54y^{53}$$