Solve (3x^2y^-3/xy)^2

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

Evaluate

$$\frac{9x^{2}}{y^{8}}$$

Solution Steps

Cancel out x in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{3x}{y^{4}}\right)^{2}$$

To raise \frac{3x}{y^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x\right)^{2}}{\left(y^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(3x\right)^{2}}{y^{8}}$$

Expand \left(3x\right)^{2}.

$$\frac{3^{2}x^{2}}{y^{8}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{2}}{y^{8}}$$

Expand

$$\frac{9x^{2}}{y^{8}}$$

Solution Steps

Cancel out x in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{3x}{y^{4}}\right)^{2}$$

To raise \frac{3x}{y^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x\right)^{2}}{\left(y^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(3x\right)^{2}}{y^{8}}$$

Expand \left(3x\right)^{2}.

$$\frac{3^{2}x^{2}}{y^{8}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{2}}{y^{8}}$$