Solve y^2*y^8*y^4=

$$y ^ { 2 } \cdot y ^ { 8 } \cdot y ^ { 4 } =$$

Evaluate

$$y^{14}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{2}y^{8}y^{4}$$

Use the Multiplication Rule for Exponents.

$$y^{2+8+4}$$

Add the exponents 2 and 8.

$$y^{10+4}$$

Add the exponents 10 and 4.

$$y^{14}$$

Differentiate w.r.t. y

$$14y^{13}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{10}y^{4})$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{14})$$

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

$$14y^{14-1}$$

Subtract 1 from 14.

$$14y^{13}$$