Solve 6r^5/2r^-4

$$\frac { 6 r ^ { 5 } } { 2 r ^ { - 4 } }$$

Evaluate

$$3r^{9}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(6r^{5}\right)^{1}\times \frac{1}{2r^{-4}}$$

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

$$6^{1}\left(r^{5}\right)^{1}\times \frac{1}{2}\times \frac{1}{r^{-4}}$$

Use the Commutative Property of Multiplication.

$$6^{1}\times \frac{1}{2}\left(r^{5}\right)^{1}\times \frac{1}{r^{-4}}$$

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

$$6^{1}\times \frac{1}{2}r^{5}r^{-4\left(-1\right)}$$

Multiply -4 times -1.

$$6^{1}\times \frac{1}{2}r^{5}r^{4}$$

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

$$6^{1}\times \frac{1}{2}r^{5+4}$$

Add the exponents 5 and 4.

$$6^{1}\times \frac{1}{2}r^{9}$$

Raise 6 to the power 1.

$$6\times \frac{1}{2}r^{9}$$

Multiply 6 times \frac{1}{2}.

$$3r^{9}$$

Differentiate w.r.t. r

$$27r^{8}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{6}{2}r^{5-\left(-4\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}r}(3r^{9})$$

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}.

$$9\times 3r^{9-1}$$

Do the arithmetic.

$$27r^{8}$$