Solve (-2xy)^5/(x^2y^-1)^-2

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

Evaluate

$$-32y^{3}x^{9}$$

Solution Steps

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

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

Calculate -2 to the power of 5 and get -32.

$$\frac{-32x^{5}y^{5}}{\left(x^{2}y^{-1}\right)^{-2}}$$

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

$$\frac{-32x^{5}y^{5}}{\left(x^{2}\right)^{-2}\left(y^{-1}\right)^{-2}}$$

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

$$\frac{-32x^{5}y^{5}}{x^{-4}\left(y^{-1}\right)^{-2}}$$

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

$$\frac{-32x^{5}y^{5}}{x^{-4}y^{2}}$$

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

$$\frac{-32y^{3}x^{5}}{x^{-4}}$$

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

$$-32y^{3}x^{9}$$

Expand

$$-32y^{3}x^{9}$$

Solution Steps

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

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

Calculate -2 to the power of 5 and get -32.

$$\frac{-32x^{5}y^{5}}{\left(x^{2}y^{-1}\right)^{-2}}$$

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

$$\frac{-32x^{5}y^{5}}{\left(x^{2}\right)^{-2}\left(y^{-1}\right)^{-2}}$$

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

$$\frac{-32x^{5}y^{5}}{x^{-4}\left(y^{-1}\right)^{-2}}$$

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

$$\frac{-32x^{5}y^{5}}{x^{-4}y^{2}}$$

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

$$\frac{-32y^{3}x^{5}}{x^{-4}}$$

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

$$-32y^{3}x^{9}$$