Solve 5n/10n^-6=

$$\frac { 5 n } { 10 n ^ { - 6 } } =$$

Evaluate

$$\frac{n^{7}}{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(5n^{1}\right)^{1}\times \frac{1}{10n^{-6}}$$

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

$$5^{1}\left(n^{1}\right)^{1}\times \frac{1}{10}\times \frac{1}{n^{-6}}$$

Use the Commutative Property of Multiplication.

$$5^{1}\times \frac{1}{10}\left(n^{1}\right)^{1}\times \frac{1}{n^{-6}}$$

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

$$5^{1}\times \frac{1}{10}n^{1}n^{-6\left(-1\right)}$$

Multiply -6 times -1.

$$5^{1}\times \frac{1}{10}n^{1}n^{6}$$

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

$$5^{1}\times \frac{1}{10}n^{1+6}$$

Add the exponents 1 and 6.

$$5^{1}\times \frac{1}{10}n^{7}$$

Raise 5 to the power 1.

$$5\times \frac{1}{10}n^{7}$$

Multiply 5 times \frac{1}{10}.

$$\frac{1}{2}n^{7}$$

Differentiate w.r.t. n

$$\frac{7n^{6}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{5}{10}n^{1-\left(-6\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{2}n^{7})$$

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}.

$$7\times \frac{1}{2}n^{7-1}$$

Do the arithmetic.

$$\frac{7}{2}n^{6}$$