Solve 8w^18/4w^6

$$\frac { 8 w ^ { 18 } } { 4 w ^ { 6 } }$$

Evaluate

$$2w^{12}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(8w^{18}\right)^{1}\times \frac{1}{4w^{6}}$$

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

$$8^{1}\left(w^{18}\right)^{1}\times \frac{1}{4}\times \frac{1}{w^{6}}$$

Use the Commutative Property of Multiplication.

$$8^{1}\times \frac{1}{4}\left(w^{18}\right)^{1}\times \frac{1}{w^{6}}$$

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

$$8^{1}\times \frac{1}{4}w^{18}w^{6\left(-1\right)}$$

Multiply 6 times -1.

$$8^{1}\times \frac{1}{4}w^{18}w^{-6}$$

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

$$8^{1}\times \frac{1}{4}w^{18-6}$$

Add the exponents 18 and -6.

$$8^{1}\times \frac{1}{4}w^{12}$$

Raise 8 to the power 1.

$$8\times \frac{1}{4}w^{12}$$

Multiply 8 times \frac{1}{4}.

$$2w^{12}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}w^{18}}{4^{1}w^{6}}$$

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

$$\frac{8^{1}w^{18-6}}{4^{1}}$$

Subtract 6 from 18.

$$\frac{8^{1}w^{12}}{4^{1}}$$

Divide 8 by 4.

$$2w^{12}$$

Differentiate w.r.t. w

$$24w^{11}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{8}{4}w^{18-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(2w^{12})$$

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}.

$$12\times 2w^{12-1}$$

Do the arithmetic.

$$24w^{11}$$