Solve -6a^3diva^-2

$$- 6 a ^ { 3 } \div a ^ { - 2 }$$

Evaluate

$$-6a^{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-6a^{3}\right)^{1}\times \frac{1}{a^{-2}}$$

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

$$\left(-6\right)^{1}\left(a^{3}\right)^{1}\times \frac{1}{1}\times \frac{1}{a^{-2}}$$

Use the Commutative Property of Multiplication.

$$\left(-6\right)^{1}\times \frac{1}{1}\left(a^{3}\right)^{1}\times \frac{1}{a^{-2}}$$

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

$$\left(-6\right)^{1}\times \frac{1}{1}a^{3}a^{-2\left(-1\right)}$$

Multiply -2 times -1.

$$\left(-6\right)^{1}\times \frac{1}{1}a^{3}a^{2}$$

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

$$\left(-6\right)^{1}\times \frac{1}{1}a^{3+2}$$

Add the exponents 3 and 2.

$$\left(-6\right)^{1}\times \frac{1}{1}a^{5}$$

Raise -6 to the power 1.

$$-6\times \frac{1}{1}a^{5}$$

Differentiate w.r.t. a

$$-30a^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{6}{1}\right)a^{3-\left(-2\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-6a^{5})$$

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}.

$$5\left(-6\right)a^{5-1}$$

Do the arithmetic.

$$-30a^{4}$$