Solve y^7*y^3*y^2

$$y ^ { 7 } \cdot y ^ { 3 } \cdot y ^ { 2 }$$

Evaluate

$$y^{12}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{7}y^{3}y^{2}$$

Use the Multiplication Rule for Exponents.

$$y^{7+3+2}$$

Add the exponents 7 and 3.

$$y^{10+2}$$

Add the exponents 10 and 2.

$$y^{12}$$

Differentiate w.r.t. y

$$12y^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{10}y^{2})$$

To multiply powers of the same base, add their exponents. Add 10 and 2 to get 12.

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

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

$$12y^{12-1}$$

Subtract 1 from 12.

$$12y^{11}$$