Solve (-2y*-2x^-1y^3/-yx^0)^-3

$$( \frac { - 2 y \cdot - 2 x ^ { - 1 } y ^ { 3 } } { - y x ^ { 0 } } ) ^ { - 3 }$$

Evaluate

$$-\frac{x^{3}}{64y^{9}}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(\frac{-2y^{4}\left(-2\right)x^{-1}}{\left(-y\right)x^{0}}\right)^{-3}$$

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

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

Multiply -2 and -2 to get 4.

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

Calculate x to the power of 1 and get x.

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

Factor the expressions that are not already factored in \frac{4y^{4}}{\left(-y\right)x}.

$$\left(\frac{4y^{4}}{-xy}\right)^{-3}$$

Cancel out y in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

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

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

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

Expand \left(-4y^{3}\right)^{-3}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{\left(-4\right)^{-3}y^{-9}}{x^{-3}}$$

Calculate -4 to the power of -3 and get -\frac{1}{64}.

$$\frac{-\frac{1}{64}y^{-9}}{x^{-3}}$$

Expand

$$-\frac{x^{3}}{64y^{9}}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(\frac{-2y^{4}\left(-2\right)x^{-1}}{\left(-y\right)x^{0}}\right)^{-3}$$

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

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

Multiply -2 and -2 to get 4.

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

Calculate x to the power of 1 and get x.

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

Factor the expressions that are not already factored in \frac{4y^{4}}{\left(-y\right)x}.

$$\left(\frac{4y^{4}}{-xy}\right)^{-3}$$

Cancel out y in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

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

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

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

Expand \left(-4y^{3}\right)^{-3}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{\left(-4\right)^{-3}y^{-9}}{x^{-3}}$$

Calculate -4 to the power of -3 and get -\frac{1}{64}.

$$\frac{-\frac{1}{64}y^{-9}}{x^{-3}}$$