Solve frac{(3x^{2}y^-2)^-3}{2x^-1y^4}=

$$\frac { ( 3 x ^ { 2 } y ^ { - 2 } ) ^ { - 3 } } { 2 x ^ { - 1 } y ^ { 4 } } =$$

Evaluate

$$\frac{y^{2}}{54x^{5}}$$

Solution Steps

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

$$\frac{3^{-3}\left(x^{2}\right)^{-3}\left(y^{-2}\right)^{-3}}{2x^{-1}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\frac{3^{-3}x^{-6}\left(y^{-2}\right)^{-3}}{2x^{-1}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

$$\frac{3^{-3}x^{-6}y^{6}}{2x^{-1}y^{4}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{1}{27}x^{-6}y^{6}}{2x^{-1}y^{4}}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{\frac{1}{27}x^{-6}y^{2}}{2\times \frac{1}{x}}$$

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

$$\frac{\frac{1}{27}y^{2}}{2x^{5}}$$

Expand

$$\frac{y^{2}}{54x^{5}}$$

Solution Steps

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

$$\frac{3^{-3}\left(x^{2}\right)^{-3}\left(y^{-2}\right)^{-3}}{2x^{-1}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\frac{3^{-3}x^{-6}\left(y^{-2}\right)^{-3}}{2x^{-1}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

$$\frac{3^{-3}x^{-6}y^{6}}{2x^{-1}y^{4}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{1}{27}x^{-6}y^{6}}{2x^{-1}y^{4}}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{\frac{1}{27}x^{-6}y^{2}}{2\times \frac{1}{x}}$$

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

$$\frac{\frac{1}{27}y^{2}}{2x^{5}}$$