Solve (2y^-frac{5{6}})^9

$$( 2 y ^ { - \frac { 5 } { 6 } } ) ^ { 9 }$$

Evaluate

$$\frac{512}{y^{\frac{15}{2}}}$$

Solution Steps

Expand \left(2y^{-\frac{5}{6}}\right)^{9}.

$$2^{9}\left(y^{-\frac{5}{6}}\right)^{9}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{5}{6} and 9 to get -\frac{15}{2}.

$$2^{9}y^{-\frac{15}{2}}$$

Calculate 2 to the power of 9 and get 512.

$$512y^{-\frac{15}{2}}$$

Expand

$$\frac{512}{y^{\frac{15}{2}}}$$

Solution Steps

Expand \left(2y^{-\frac{5}{6}}\right)^{9}.

$$2^{9}\left(y^{-\frac{5}{6}}\right)^{9}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{5}{6} and 9 to get -\frac{15}{2}.

$$2^{9}y^{-\frac{15}{2}}$$

Calculate 2 to the power of 9 and get 512.

$$512y^{-\frac{15}{2}}$$