Solve -16d^2/(-8d^8)

$$\frac { - 16 d ^ { 2 } } { ( - 8 d ^ { 8 } ) }$$

Evaluate

$$\frac{2}{d^{6}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-16d^{2}\right)^{1}\times \frac{1}{-8d^{8}}$$

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

$$\left(-16\right)^{1}\left(d^{2}\right)^{1}\times \frac{1}{-8}\times \frac{1}{d^{8}}$$

Use the Commutative Property of Multiplication.

$$\left(-16\right)^{1}\times \frac{1}{-8}\left(d^{2}\right)^{1}\times \frac{1}{d^{8}}$$

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

$$\left(-16\right)^{1}\times \frac{1}{-8}d^{2}d^{8\left(-1\right)}$$

Multiply 8 times -1.

$$\left(-16\right)^{1}\times \frac{1}{-8}d^{2}d^{-8}$$

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

$$\left(-16\right)^{1}\times \frac{1}{-8}d^{2-8}$$

Add the exponents 2 and -8.

$$\left(-16\right)^{1}\times \frac{1}{-8}d^{-6}$$

Raise -16 to the power 1.

$$-16\times \frac{1}{-8}d^{-6}$$

Raise -8 to the power -1.

$$-16\left(-\frac{1}{8}\right)d^{-6}$$

Multiply -16 times -\frac{1}{8}.

$$2d^{-6}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-16\right)^{1}d^{2}}{\left(-8\right)^{1}d^{8}}$$

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

$$\frac{\left(-16\right)^{1}d^{2-8}}{\left(-8\right)^{1}}$$

Subtract 8 from 2.

$$\frac{\left(-16\right)^{1}d^{-6}}{\left(-8\right)^{1}}$$

Divide -16 by -8.

$$2d^{-6}$$

Differentiate w.r.t. d

$$-\frac{12}{d^{7}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}d}(\left(-\frac{16}{-8}\right)d^{2-8})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}d}(2d^{-6})$$

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}.

$$-6\times 2d^{-6-1}$$

Do the arithmetic.

$$-12d^{-7}$$