Solve 42w^5/35w^2

$$\frac { 42 w ^ { 5 } } { 35 w ^ { 2 } }$$

Evaluate

$$\frac{6w^{3}}{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(42w^{5}\right)^{1}\times \frac{1}{35w^{2}}$$

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

$$42^{1}\left(w^{5}\right)^{1}\times \frac{1}{35}\times \frac{1}{w^{2}}$$

Use the Commutative Property of Multiplication.

$$42^{1}\times \frac{1}{35}\left(w^{5}\right)^{1}\times \frac{1}{w^{2}}$$

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

$$42^{1}\times \frac{1}{35}w^{5}w^{2\left(-1\right)}$$

Multiply 2 times -1.

$$42^{1}\times \frac{1}{35}w^{5}w^{-2}$$

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

$$42^{1}\times \frac{1}{35}w^{5-2}$$

Add the exponents 5 and -2.

$$42^{1}\times \frac{1}{35}w^{3}$$

Raise 42 to the power 1.

$$42\times \frac{1}{35}w^{3}$$

Multiply 42 times \frac{1}{35}.

$$\frac{6}{5}w^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{42^{1}w^{5}}{35^{1}w^{2}}$$

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

$$\frac{42^{1}w^{5-2}}{35^{1}}$$

Subtract 2 from 5.

$$\frac{42^{1}w^{3}}{35^{1}}$$

Reduce the fraction \frac{42}{35} to lowest terms by extracting and canceling out 7.

$$\frac{6}{5}w^{3}$$

Differentiate w.r.t. w

$$\frac{18w^{2}}{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{42}{35}w^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{6}{5}w^{3})$$

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}.

$$3\times \frac{6}{5}w^{3-1}$$

Do the arithmetic.

$$\frac{18}{5}w^{2}$$