Solve y*y^4*y^-2

$$y \times y ^ { 4 } \times y ^ { - 2 }$$

Evaluate

$$y^{3}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{1}y^{4}y^{-2}$$

Use the Multiplication Rule for Exponents.

$$y^{1+4-2}$$

Add the exponents 1 and 4.

$$y^{5-2}$$

Add the exponents 5 and -2.

$$y^{3}$$

Differentiate w.r.t. y

$$3y^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{5}y^{-2})$$

To multiply powers of the same base, add their exponents. Add 5 and -2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{3})$$

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

$$3y^{3-1}$$

Subtract 1 from 3.

$$3y^{2}$$