Solve 6u^-1/3u^8

$$\frac { 6 u ^ { - 1 } } { 3 u ^ { 8 } }$$

Evaluate

$$\frac{2}{u^{9}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(6\times \frac{1}{u}\right)^{1}\times \frac{1}{3u^{8}}$$

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

$$6^{1}\times \left(\frac{1}{u}\right)^{1}\times \frac{1}{3}\times \frac{1}{u^{8}}$$

Use the Commutative Property of Multiplication.

$$6^{1}\times \frac{1}{3}\times \left(\frac{1}{u}\right)^{1}\times \frac{1}{u^{8}}$$

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

$$6^{1}\times \frac{1}{3}\times \frac{1}{u}u^{8\left(-1\right)}$$

Multiply 8 times -1.

$$6^{1}\times \frac{1}{3}\times \frac{1}{u}u^{-8}$$

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

$$6^{1}\times \frac{1}{3}u^{-1-8}$$

Add the exponents -1 and -8.

$$6^{1}\times \frac{1}{3}u^{-9}$$

Raise 6 to the power 1.

$$6\times \frac{1}{3}u^{-9}$$

Multiply 6 times \frac{1}{3}.

$$2u^{-9}$$

Differentiate w.r.t. u

$$-\frac{18}{u^{10}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{6}{3}u^{-1-8})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(2u^{-9})$$

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}.

$$-9\times 2u^{-9-1}$$

Do the arithmetic.

$$-18u^{-10}$$