Solve y^4*y*y^-9

$$y ^ { 4 } \cdot y \cdot y ^ { - 9 }$$

Evaluate

$$\frac{1}{y^{4}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{4}y^{1}y^{-9}$$

Use the Multiplication Rule for Exponents.

$$y^{4+1-9}$$

Add the exponents 4 and 1.

$$y^{5-9}$$

Add the exponents 5 and -9.

$$y^{-4}$$

Differentiate w.r.t. y

$$-\frac{4}{y^{5}}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{5}y^{-9})$$

To multiply powers of the same base, add their exponents. Add 5 and -9 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{-4})$$

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

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

Subtract 1 from -4.

$$-4y^{-5}$$