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

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

Evaluate

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

Use the Multiplication Rule for Exponents.

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

Add the exponents -5 and 10.

$$y^{5-6}$$

Add the exponents 5 and -6.

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

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 -5 and 10 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{5}y^{-6})$$

To multiply powers of the same base, add their exponents. Add 5 and -6 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.

$$-y^{-2}$$