Solve y^-2*y^4*y^-3

$$y ^ { - 2 } \cdot y ^ { 4 } \cdot y ^ { - 3 }$$

Evaluate

$$\frac{1}{y}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{-2}y^{4}y^{-3}$$

Use the Multiplication Rule for Exponents.

$$y^{-2+4-3}$$

Add the exponents -2 and 4.

$$y^{2-3}$$

Add the exponents 2 and -3.

$$\frac{1}{y}$$

Differentiate w.r.t. y

$$-\frac{1}{y^{2}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -2 and 4 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{2}y^{-3})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{-1})$$

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

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

Subtract 1 from -1.

$$-y^{-2}$$