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

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

Evaluate

$$\frac{9}{y^{2}x^{4}}$$

Solution Steps

Cancel out 3^{2}y^{2} in both numerator and denominator.

$$\left(\frac{xy}{3\times \frac{1}{x}}\right)^{-2}$$

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

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

To raise \frac{yx^{2}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(yx^{2}\right)^{-2}.

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

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

$$\frac{y^{-2}x^{-4}}{3^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{y^{-2}x^{-4}}{\frac{1}{9}}$$

Divide y^{-2}x^{-4} by \frac{1}{9} by multiplying y^{-2}x^{-4} by the reciprocal of \frac{1}{9}.

$$y^{-2}x^{-4}\times 9$$

Expand

$$\frac{9}{y^{2}x^{4}}$$

Solution Steps

Cancel out 3^{2}y^{2} in both numerator and denominator.

$$\left(\frac{xy}{3\times \frac{1}{x}}\right)^{-2}$$

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

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

To raise \frac{yx^{2}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(yx^{2}\right)^{-2}.

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

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

$$\frac{y^{-2}x^{-4}}{3^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{y^{-2}x^{-4}}{\frac{1}{9}}$$

Divide y^{-2}x^{-4} by \frac{1}{9} by multiplying y^{-2}x^{-4} by the reciprocal of \frac{1}{9}.

$$y^{-2}x^{-4}\times 9$$