Solve (3w^frac{7{6}})^-4

$$( 3 w ^ { \frac { 7 } { 6 } } ) ^ { - 4 }$$

Evaluate

$$\frac{1}{81w^{\frac{14}{3}}}$$

Solution Steps

Expand \left(3w^{\frac{7}{6}}\right)^{-4}.

$$3^{-4}\left(w^{\frac{7}{6}}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{6} and -4 to get -\frac{14}{3}.

$$3^{-4}w^{-\frac{14}{3}}$$

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\frac{1}{81}w^{-\frac{14}{3}}$$

Expand

$$\frac{1}{81w^{\frac{14}{3}}}$$

Solution Steps

Expand \left(3w^{\frac{7}{6}}\right)^{-4}.

$$3^{-4}\left(w^{\frac{7}{6}}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{6} and -4 to get -\frac{14}{3}.

$$3^{-4}w^{-\frac{14}{3}}$$

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\frac{1}{81}w^{-\frac{14}{3}}$$