Solve -a^2015*(1/a)^2016

$$- a ^ { 2015 } \cdot ( \frac { 1 } { a } ) ^ { 2016 }$$

Evaluate

$$-\frac{1}{a}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-a^{2015}\right)^{1}\times \left(\frac{1}{a}\right)^{2016}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$-\left(a^{2015}\right)^{1}\times 1^{2016}\times \left(\frac{1}{a}\right)^{2016}$$

Use the Commutative Property of Multiplication.

$$-1^{2016}\left(a^{2015}\right)^{1}\times \left(\frac{1}{a}\right)^{2016}$$

To raise a power to another power, multiply the exponents.

$$-1^{2016}a^{2015}a^{-2016}$$

To multiply powers of the same base, add their exponents.

$$-1^{2016}a^{2015-2016}$$

Add the exponents 2015 and -2016.

$$-1^{2016}\times \frac{1}{a}$$

Differentiate w.r.t. a

$$\frac{1}{a^{2}}$$

Steps Using Definition of a Derivative

To raise \frac{1}{a} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-a^{2015}\right)\times \frac{1^{2016}}{a^{2016}})$$

Express \left(-a^{2015}\right)\times \frac{1^{2016}}{a^{2016}} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-a^{2015}\times 1^{2016}}{a^{2016}})$$

Cancel out a^{2015} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-1^{2016}}{a})$$

Calculate 1 to the power of 2016 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-1}{a})$$

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

$$-\left(-1\right)a^{-1-1}$$

Multiply -1 times -1.

$$a^{-1-1}$$

Subtract 1 from -1.

$$a^{-2}$$