Solve (z^frac{3{2}}*y^frac{1{2}})^-3

$$( z ^ { \frac { 3 } { 2 } } \cdot y ^ { \frac { 1 } { 2 } } ) ^ { - 3 }$$

Evaluate

$$\frac{1}{y^{\frac{3}{2}}z^{\frac{9}{2}}}$$

Solution Steps

Expand \left(z^{\frac{3}{2}}y^{\frac{1}{2}}\right)^{-3}.

$$\left(z^{\frac{3}{2}}\right)^{-3}\left(y^{\frac{1}{2}}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{2} and -3 to get -\frac{9}{2}.

$$z^{-\frac{9}{2}}\left(y^{\frac{1}{2}}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and -3 to get -\frac{3}{2}.

$$z^{-\frac{9}{2}}y^{-\frac{3}{2}}$$

Expand

$$\frac{1}{y^{\frac{3}{2}}z^{\frac{9}{2}}}$$

Solution Steps

Expand \left(z^{\frac{3}{2}}y^{\frac{1}{2}}\right)^{-3}.

$$\left(z^{\frac{3}{2}}\right)^{-3}\left(y^{\frac{1}{2}}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{2} and -3 to get -\frac{9}{2}.

$$z^{-\frac{9}{2}}\left(y^{\frac{1}{2}}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and -3 to get -\frac{3}{2}.

$$z^{-\frac{9}{2}}y^{-\frac{3}{2}}$$