Solve -6n^8/15n^5

$$\frac { - 6 n ^ { 8 } } { 15 n ^ { 5 } }$$

Evaluate

$$-\frac{2n^{3}}{5}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-6n^{8}\right)^{1}\times \frac{1}{15n^{5}}$$

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

$$\left(-6\right)^{1}\left(n^{8}\right)^{1}\times \frac{1}{15}\times \frac{1}{n^{5}}$$

Use the Commutative Property of Multiplication.

$$\left(-6\right)^{1}\times \frac{1}{15}\left(n^{8}\right)^{1}\times \frac{1}{n^{5}}$$

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

$$\left(-6\right)^{1}\times \frac{1}{15}n^{8}n^{5\left(-1\right)}$$

Multiply 5 times -1.

$$\left(-6\right)^{1}\times \frac{1}{15}n^{8}n^{-5}$$

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

$$\left(-6\right)^{1}\times \frac{1}{15}n^{8-5}$$

Add the exponents 8 and -5.

$$\left(-6\right)^{1}\times \frac{1}{15}n^{3}$$

Raise -6 to the power 1.

$$-6\times \frac{1}{15}n^{3}$$

Multiply -6 times \frac{1}{15}.

$$-\frac{2}{5}n^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-6\right)^{1}n^{8}}{15^{1}n^{5}}$$

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

$$\frac{\left(-6\right)^{1}n^{8-5}}{15^{1}}$$

Subtract 5 from 8.

$$\frac{\left(-6\right)^{1}n^{3}}{15^{1}}$$

Reduce the fraction \frac{-6}{15} to lowest terms by extracting and canceling out 3.

$$-\frac{2}{5}n^{3}$$

Differentiate w.r.t. n

$$-\frac{6n^{2}}{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\left(-\frac{6}{15}\right)n^{8-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(-\frac{2}{5}n^{3})$$

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}.

$$3\left(-\frac{2}{5}\right)n^{3-1}$$

Do the arithmetic.

$$-\frac{6}{5}n^{2}$$