Solve (2r^frac{3{4}})^7

$$( 2 r ^ { \frac { 3 } { 4 } } ) ^ { 7 }$$

Evaluate

$$128r^{\frac{21}{4}}$$

Solution Steps

Expand \left(2r^{\frac{3}{4}}\right)^{7}.

$$2^{7}\left(r^{\frac{3}{4}}\right)^{7}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{4} and 7 to get \frac{21}{4}.

$$2^{7}r^{\frac{21}{4}}$$

Calculate 2 to the power of 7 and get 128.

$$128r^{\frac{21}{4}}$$

Expand

$$128r^{\frac{21}{4}}$$

Solution Steps

Expand \left(2r^{\frac{3}{4}}\right)^{7}.

$$2^{7}\left(r^{\frac{3}{4}}\right)^{7}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{4} and 7 to get \frac{21}{4}.

$$2^{7}r^{\frac{21}{4}}$$

Calculate 2 to the power of 7 and get 128.

$$128r^{\frac{21}{4}}$$