Solve y^2*y*y^5

$${ y }^{ 2 } \times y \times { y }^{ 5 }$$

Evaluate

$$y^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{2}y^{1}y^{5}$$

Use the Multiplication Rule for Exponents.

$$y^{2+1+5}$$

Add the exponents 2 and 1.

$$y^{3+5}$$

Add the exponents 3 and 5.

$$y^{8}$$

Differentiate w.r.t. y

$$8y^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{3}y^{5})$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

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

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

$$8y^{8-1}$$

Subtract 1 from 8.

$$8y^{7}$$