Solve -5a/-a^5=

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

Evaluate

$$\frac{5}{a^{4}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply 5 times -1.

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

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

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

Add the exponents 1 and -5.

$$\left(-5\right)^{1}\left(-1\right)a^{-4}$$

Raise -5 to the power 1.

$$-5\left(-1\right)a^{-4}$$

Multiply -5 times -1.

$$5a^{-4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 5 from 1.

$$\frac{\left(-5\right)^{1}a^{-4}}{-1}$$

Divide -5 by -1.

$$5a^{-4}$$

Differentiate w.r.t. a

$$-\frac{20}{a^{5}}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5a^{-4})$$

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}.

$$-4\times 5a^{-4-1}$$

Do the arithmetic.

$$-20a^{-5}$$