Solve (16c^4d^3)^frac{3{4}}

$$( 16 c ^ { 4 } d ^ { 3 } ) ^ { \frac { 3 } { 4 } }$$

Evaluate

$$8\left(d^{3}c^{4}\right)^{\frac{3}{4}}$$

Solution Steps

Expand \left(16c^{4}d^{3}\right)^{\frac{3}{4}}.

$$16^{\frac{3}{4}}\left(c^{4}\right)^{\frac{3}{4}}\left(d^{3}\right)^{\frac{3}{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and \frac{3}{4} to get 3.

$$16^{\frac{3}{4}}c^{3}\left(d^{3}\right)^{\frac{3}{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and \frac{3}{4} to get \frac{9}{4}.

$$16^{\frac{3}{4}}c^{3}d^{\frac{9}{4}}$$

Calculate 16 to the power of \frac{3}{4} and get 8.

$$8c^{3}d^{\frac{9}{4}}$$

Differentiate w.r.t. c

$$\frac{24d^{\frac{9}{4}}c^{3}}{|c|}$$