Solve (2v^frac{7{4}})^6

$$( 2 v ^ { \frac { 7 } { 4 } } ) ^ { 6 }$$

Evaluate

$$64v^{\frac{21}{2}}$$

Solution Steps

Expand \left(2v^{\frac{7}{4}}\right)^{6}.

$$2^{6}\left(v^{\frac{7}{4}}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{4} and 6 to get \frac{21}{2}.

$$2^{6}v^{\frac{21}{2}}$$

Calculate 2 to the power of 6 and get 64.

$$64v^{\frac{21}{2}}$$

Expand

$$64v^{\frac{21}{2}}$$

Solution Steps

Expand \left(2v^{\frac{7}{4}}\right)^{6}.

$$2^{6}\left(v^{\frac{7}{4}}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{4} and 6 to get \frac{21}{2}.

$$2^{6}v^{\frac{21}{2}}$$

Calculate 2 to the power of 6 and get 64.

$$64v^{\frac{21}{2}}$$