Solve (-3xy^-2)^-5/(xy^-1)^-2

$$\frac { ( - 3 x y ^ { - 2 } ) ^ { - 5 } } { ( x y ^ { - 1 } ) ^ { - 2 } }$$

Evaluate

$$-\frac{y^{8}}{243x^{3}}$$

Solution Steps

Expand \left(-3xy^{-2}\right)^{-5}.

$$\frac{\left(-3\right)^{-5}x^{-5}\left(y^{-2}\right)^{-5}}{\left(xy^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -5 to get 10.

$$\frac{\left(-3\right)^{-5}x^{-5}y^{10}}{\left(xy^{-1}\right)^{-2}}$$

Calculate -3 to the power of -5 and get -\frac{1}{243}.

$$\frac{-\frac{1}{243}x^{-5}y^{10}}{\left(xy^{-1}\right)^{-2}}$$

Expand \left(xy^{-1}\right)^{-2}.

$$\frac{-\frac{1}{243}x^{-5}y^{10}}{x^{-2}\left(y^{-1}\right)^{-2}}$$

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

$$\frac{-\frac{1}{243}x^{-5}y^{10}}{x^{-2}y^{2}}$$

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

$$\frac{-\frac{1}{243}x^{-5}y^{8}}{x^{-2}}$$

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

$$\frac{-\frac{1}{243}y^{8}}{x^{3}}$$

Expand

$$-\frac{y^{8}}{243x^{3}}$$

Solution Steps

Expand \left(-3xy^{-2}\right)^{-5}.

$$\frac{\left(-3\right)^{-5}x^{-5}\left(y^{-2}\right)^{-5}}{\left(xy^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -5 to get 10.

$$\frac{\left(-3\right)^{-5}x^{-5}y^{10}}{\left(xy^{-1}\right)^{-2}}$$

Calculate -3 to the power of -5 and get -\frac{1}{243}.

$$\frac{-\frac{1}{243}x^{-5}y^{10}}{\left(xy^{-1}\right)^{-2}}$$

Expand \left(xy^{-1}\right)^{-2}.

$$\frac{-\frac{1}{243}x^{-5}y^{10}}{x^{-2}\left(y^{-1}\right)^{-2}}$$

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

$$\frac{-\frac{1}{243}x^{-5}y^{10}}{x^{-2}y^{2}}$$

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

$$\frac{-\frac{1}{243}x^{-5}y^{8}}{x^{-2}}$$

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

$$\frac{-\frac{1}{243}y^{8}}{x^{3}}$$