Solve (y^-5)^-10y^10

$$( y ^ { - 5 } ) ^ { - 10 } y ^ { 10 }$$

Evaluate

$$y^{60}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -5 and -10 to get 50.

$$y^{50}y^{10}$$

To multiply powers of the same base, add their exponents. Add 50 and 10 to get 60.

$$y^{60}$$

Differentiate w.r.t. y

$$60y^{59}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply -5 and -10 to get 50.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{50}y^{10})$$

To multiply powers of the same base, add their exponents. Add 50 and 10 to get 60.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{60})$$

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

$$60y^{60-1}$$

Subtract 1 from 60.

$$60y^{59}$$