Solve -a^3/-a^2

$$\frac{ - { a }^{ 3 } }{ - { a }^{ 2 } }$$

Evaluate

$$a$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-a^{3}\right)^{1}\times \frac{1}{-a^{2}}$$

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

$$-\left(a^{3}\right)^{1}\left(-1\right)\times \frac{1}{a^{2}}$$

Use the Commutative Property of Multiplication.

$$-\left(-1\right)\left(a^{3}\right)^{1}\times \frac{1}{a^{2}}$$

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

$$-\left(-1\right)a^{3}a^{2\left(-1\right)}$$

Multiply 2 times -1.

$$-\left(-1\right)a^{3}a^{-2}$$

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

$$-\left(-1\right)a^{3-2}$$

Add the exponents 3 and -2.

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

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

$$a^{1}$$

For any term t, t^{1}=t.

$$a$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{-a^{3}}{-a^{2}}$$

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

$$a^{3-2}$$

Subtract 2 from 3.

$$a^{1}$$

For any term t, t^{1}=t.

$$a$$

Differentiate w.r.t. a

$$1$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{1}{-1}\right)a^{3-2})$$

Do the arithmetic.

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

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}.

$$a^{1-1}$$

Do the arithmetic.

$$a^{0}$$

For any term t except 0, t^{0}=1.

$$1$$