Solve y^-6*y^18*y^6

$$y ^ { - 6 } \cdot y ^ { 18 } \cdot y ^ { 6 }$$

Evaluate

$$y^{18}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{-6}y^{18}y^{6}$$

Use the Multiplication Rule for Exponents.

$$y^{-6+18+6}$$

Add the exponents -6 and 18.

$$y^{12+6}$$

Add the exponents 12 and 6.

$$y^{18}$$

Differentiate w.r.t. y

$$18y^{17}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -6 and 18 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{12}y^{6})$$

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{18})$$

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

$$18y^{18-1}$$

Subtract 1 from 18.

$$18y^{17}$$