Solve (frac{xy^-frac{1{2}}}{9x^frac{3{2}}})^2

$$( \frac { x y ^ { - \frac { 1 } { 2 } } } { 9 x ^ { \frac { 3 } { 2 } } } ) ^ { 2 }$$

Evaluate

$$\frac{1}{81xy}$$

Short Solution Steps

Cancel out x in both numerator and denominator.

$$\left(\frac{y^{-\frac{1}{2}}}{9\sqrt{x}}\right)^{2}$$

To raise \frac{y^{-\frac{1}{2}}}{9\sqrt{x}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(y^{-\frac{1}{2}}\right)^{2}}{\left(9\sqrt{x}\right)^{2}}$$

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

$$\frac{y^{-1}}{\left(9\sqrt{x}\right)^{2}}$$

Expand \left(9\sqrt{x}\right)^{2}.

$$\frac{y^{-1}}{9^{2}\left(\sqrt{x}\right)^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{y^{-1}}{81\left(\sqrt{x}\right)^{2}}$$

Calculate \sqrt{x} to the power of 2 and get x.

$$\frac{y^{-1}}{81x}$$

Expand

$$\frac{1}{81xy}$$

Short Solution Steps

Cancel out x in both numerator and denominator.

$$\left(\frac{y^{-\frac{1}{2}}}{9\sqrt{x}}\right)^{2}$$

To raise \frac{y^{-\frac{1}{2}}}{9\sqrt{x}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(y^{-\frac{1}{2}}\right)^{2}}{\left(9\sqrt{x}\right)^{2}}$$

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

$$\frac{y^{-1}}{\left(9\sqrt{x}\right)^{2}}$$

Expand \left(9\sqrt{x}\right)^{2}.

$$\frac{y^{-1}}{9^{2}\left(\sqrt{x}\right)^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{y^{-1}}{81\left(\sqrt{x}\right)^{2}}$$

Calculate \sqrt{x} to the power of 2 and get x.

$$\frac{y^{-1}}{81x}$$