Solve 5u^7/30u^4

$$\frac { 5 u ^ { 7 } } { 30 u ^ { 4 } }$$

Evaluate

$$\frac{u^{3}}{6}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(5u^{7}\right)^{1}\times \frac{1}{30u^{4}}$$

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

$$5^{1}\left(u^{7}\right)^{1}\times \frac{1}{30}\times \frac{1}{u^{4}}$$

Use the Commutative Property of Multiplication.

$$5^{1}\times \frac{1}{30}\left(u^{7}\right)^{1}\times \frac{1}{u^{4}}$$

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

$$5^{1}\times \frac{1}{30}u^{7}u^{4\left(-1\right)}$$

Multiply 4 times -1.

$$5^{1}\times \frac{1}{30}u^{7}u^{-4}$$

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

$$5^{1}\times \frac{1}{30}u^{7-4}$$

Add the exponents 7 and -4.

$$5^{1}\times \frac{1}{30}u^{3}$$

Raise 5 to the power 1.

$$5\times \frac{1}{30}u^{3}$$

Multiply 5 times \frac{1}{30}.

$$\frac{1}{6}u^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{5^{1}u^{7}}{30^{1}u^{4}}$$

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

$$\frac{5^{1}u^{7-4}}{30^{1}}$$

Subtract 4 from 7.

$$\frac{5^{1}u^{3}}{30^{1}}$$

Reduce the fraction \frac{5}{30} to lowest terms by extracting and canceling out 5.

$$\frac{1}{6}u^{3}$$

Differentiate w.r.t. u

$$\frac{u^{2}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{5}{30}u^{7-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{1}{6}u^{3})$$

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}.

$$3\times \frac{1}{6}u^{3-1}$$

Do the arithmetic.

$$\frac{1}{2}u^{2}$$