Solve (y^2)^6*(y)^4

$$( y ^ { 2 } ) ^ { 6 } \times ( y ) ^ { 4 }$$

Evaluate

$$y^{16}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$y^{12}y^{4}$$

To multiply powers of the same base, add their exponents. Add 12 and 4 to get 16.

$$y^{16}$$

Differentiate w.r.t. y

$$16y^{15}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{12}y^{4})$$

To multiply powers of the same base, add their exponents. Add 12 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{16})$$

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

$$16y^{16-1}$$

Subtract 1 from 16.

$$16y^{15}$$