Solve a^10/-a^2

$$\frac { a ^ { 10 } } { - a ^ { 2 } }$$

Evaluate

$$-a^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(a^{1}\right)^{10}\times \frac{1}{-a^{2}}$$

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

$$1^{10}\left(a^{1}\right)^{10}\left(-1\right)\times \frac{1}{a^{2}}$$

Use the Commutative Property of Multiplication.

$$1^{10}\left(-1\right)\left(a^{1}\right)^{10}\times \frac{1}{a^{2}}$$

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

$$1^{10}\left(-1\right)a^{10}a^{2\left(-1\right)}$$

Multiply 2 times -1.

$$1^{10}\left(-1\right)a^{10}a^{-2}$$

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

$$1^{10}\left(-1\right)a^{10-2}$$

Add the exponents 10 and -2.

$$1^{10}\left(-1\right)a^{8}$$

Raise -1 to the power -1.

$$-a^{8}$$

Differentiate w.r.t. a

$$-8a^{7}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{-1}a^{10-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a^{8})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$8\left(-1\right)a^{8-1}$$

Do the arithmetic.

$$-8a^{7}$$