Solve (bc^3)^frac{1{5}}

$$( b c ^ { 3 } ) ^ { \frac { 1 } { 5 } }$$

Evaluate

$$\sqrt[5]{b}c^{\frac{3}{5}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\sqrt[5]{b^{1}c^{3}}$$

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

$$\sqrt[5]{b^{1}}\sqrt[5]{c^{3}}$$

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

$$\sqrt[5]{b}c^{3\times \frac{1}{5}}$$

Multiply 3 times \frac{1}{5}.

$$\sqrt[5]{b}c^{\frac{3}{5}}$$

Differentiate w.r.t. b

$$\frac{c^{\frac{3}{5}}}{5b^{\frac{4}{5}}}$$