Solve (3w^frac{7{5}})^4

$$( 3 w ^ { \frac { 7 } { 5 } } ) ^ { 4 }$$

Evaluate

$$81w^{\frac{28}{5}}$$

Solution Steps

Expand \left(3w^{\frac{7}{5}}\right)^{4}.

$$3^{4}\left(w^{\frac{7}{5}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{5} and 4 to get \frac{28}{5}.

$$3^{4}w^{\frac{28}{5}}$$

Calculate 3 to the power of 4 and get 81.

$$81w^{\frac{28}{5}}$$

Expand

$$81w^{\frac{28}{5}}$$

Solution Steps

Expand \left(3w^{\frac{7}{5}}\right)^{4}.

$$3^{4}\left(w^{\frac{7}{5}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{5} and 4 to get \frac{28}{5}.

$$3^{4}w^{\frac{28}{5}}$$

Calculate 3 to the power of 4 and get 81.

$$81w^{\frac{28}{5}}$$