Solve yy^6y^8

$$y { y }^{ 6 } { y }^{ 8 }$$

Evaluate

$$y^{15}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{1}y^{6}y^{8}$$

Use the Multiplication Rule for Exponents.

$$y^{1+6+8}$$

Add the exponents 1 and 6.

$$y^{7+8}$$

Add the exponents 7 and 8.

$$y^{15}$$

Differentiate w.r.t. y

$$15y^{14}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{7}y^{8})$$

To multiply powers of the same base, add their exponents. Add 7 and 8 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{15})$$

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

$$15y^{15-1}$$

Subtract 1 from 15.

$$15y^{14}$$