Solve (-2a^12)diva^4

$$( - 2 a ^ { 12 } ) \div a ^ { 4 }$$

Evaluate

$$-2a^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-2a^{12}\right)^{1}\times \frac{1}{a^{4}}$$

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

$$\left(-2\right)^{1}\left(a^{12}\right)^{1}\times \frac{1}{1}\times \frac{1}{a^{4}}$$

Use the Commutative Property of Multiplication.

$$\left(-2\right)^{1}\times \frac{1}{1}\left(a^{12}\right)^{1}\times \frac{1}{a^{4}}$$

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

$$\left(-2\right)^{1}\times \frac{1}{1}a^{12}a^{4\left(-1\right)}$$

Multiply 4 times -1.

$$\left(-2\right)^{1}\times \frac{1}{1}a^{12}a^{-4}$$

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

$$\left(-2\right)^{1}\times \frac{1}{1}a^{12-4}$$

Add the exponents 12 and -4.

$$\left(-2\right)^{1}\times \frac{1}{1}a^{8}$$

Raise -2 to the power 1.

$$-2\times \frac{1}{1}a^{8}$$

Differentiate w.r.t. a

$$-16a^{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{2}{1}\right)a^{12-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-2a^{8})$$

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}.

$$8\left(-2\right)a^{8-1}$$

Do the arithmetic.

$$-16a^{7}$$