Solve (16/n^11)^1/7

$$( \frac { 16 } { n ^ { 11 } } ) ^ { 1 / 7 }$$

Evaluate

$$\frac{2^{\frac{4}{7}}}{n^{\frac{11}{7}}}$$

Steps for Raising Quotient to a Power

Use the rules of exponents to simplify the expression.

$$\sqrt[7]{\frac{16}{n^{11}}}$$

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

$$\frac{\sqrt[7]{16}}{\sqrt[7]{n^{11}}}$$

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

$$\frac{2^{\frac{4}{7}}}{n^{11\times \frac{1}{7}}}$$

Multiply 11 times \frac{1}{7}.

$$\frac{2^{\frac{4}{7}}}{n^{\frac{11}{7}}}$$

Differentiate w.r.t. n

$$-\frac{11\times 2^{\frac{4}{7}}}{7n^{\frac{18}{7}}}$$