Solve (27vw^3)^-frac{1{3}}

$$( 27 v w ^ { 3 } ) ^ { - \frac { 1 } { 3 } }$$

Evaluate

$$\frac{1}{3\sqrt[3]{v}w}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(27v^{1}w^{3}\right)^{-\frac{1}{3}}$$

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

$$27^{-\frac{1}{3}}\left(v^{1}\right)^{-\frac{1}{3}}\left(w^{3}\right)^{-\frac{1}{3}}$$

Raise 27 to the power -\frac{1}{3}.

$$\frac{1}{3}\left(v^{1}\right)^{-\frac{1}{3}}\left(w^{3}\right)^{-\frac{1}{3}}$$

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

$$\frac{1}{3}v^{-\frac{1}{3}}w^{3\left(-\frac{1}{3}\right)}$$

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

$$\frac{1}{3}\times \frac{1}{\sqrt[3]{v}}\times \frac{1}{w}$$

Differentiate w.r.t. v

$$-\frac{1}{9wv^{\frac{4}{3}}}$$