Solve 36w^4/63w^6

$$\frac { 36 w ^ { 4 } } { 63 w ^ { 6 } }$$

Evaluate

$$\frac{4}{7w^{2}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(36w^{4}\right)^{1}\times \frac{1}{63w^{6}}$$

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

$$36^{1}\left(w^{4}\right)^{1}\times \frac{1}{63}\times \frac{1}{w^{6}}$$

Use the Commutative Property of Multiplication.

$$36^{1}\times \frac{1}{63}\left(w^{4}\right)^{1}\times \frac{1}{w^{6}}$$

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

$$36^{1}\times \frac{1}{63}w^{4}w^{6\left(-1\right)}$$

Multiply 6 times -1.

$$36^{1}\times \frac{1}{63}w^{4}w^{-6}$$

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

$$36^{1}\times \frac{1}{63}w^{4-6}$$

Add the exponents 4 and -6.

$$36^{1}\times \frac{1}{63}w^{-2}$$

Raise 36 to the power 1.

$$36\times \frac{1}{63}w^{-2}$$

Multiply 36 times \frac{1}{63}.

$$\frac{4}{7}w^{-2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{36^{1}w^{4}}{63^{1}w^{6}}$$

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

$$\frac{36^{1}w^{4-6}}{63^{1}}$$

Subtract 6 from 4.

$$\frac{36^{1}w^{-2}}{63^{1}}$$

Reduce the fraction \frac{36}{63} to lowest terms by extracting and canceling out 9.

$$\frac{4}{7}w^{-2}$$

Differentiate w.r.t. w

$$-\frac{8}{7w^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{36}{63}w^{4-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{4}{7}w^{-2})$$

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}.

$$-2\times \frac{4}{7}w^{-2-1}$$

Do the arithmetic.

$$-\frac{8}{7}w^{-3}$$