Solve =-a^5/-a^-3

$$= \frac { - a ^ { 5 } } { - a ^ { - 3 } }$$

Evaluate

$$a^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-a^{5}\right)^{1}\times \frac{1}{-a^{-3}}$$

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

$$-\left(a^{5}\right)^{1}\left(-1\right)\times \frac{1}{a^{-3}}$$

Use the Commutative Property of Multiplication.

$$-\left(-1\right)\left(a^{5}\right)^{1}\times \frac{1}{a^{-3}}$$

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

$$-\left(-1\right)a^{5}a^{-3\left(-1\right)}$$

Multiply -3 times -1.

$$-\left(-1\right)a^{5}a^{3}$$

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

$$-\left(-1\right)a^{5+3}$$

Add the exponents 5 and 3.

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

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

$$a^{8}$$

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.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{1}{-1}\right)a^{5-\left(-3\right)})$$

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}.

$$8a^{8-1}$$

Do the arithmetic.

$$8a^{7}$$