Solve y^-6*y^10*y^-5

$$y ^ { - 6 } \cdot y ^ { 10 } \cdot y ^ { - 5 }$$

Evaluate

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$y^{-6}y^{10}y^{-5}$$

Use the Multiplication Rule for Exponents.

$$y^{-6+10-5}$$

Add the exponents -6 and 10.

$$y^{4-5}$$

Add the exponents 4 and -5.

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

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 -6 and 10 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{4}y^{-5})$$

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

$$-y^{-2}$$