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

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

Evaluate

$$-\frac{8}{z^{3}x^{12}}$$

Solution Steps

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

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

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

$$\left(\frac{-2}{zx^{4}}\right)^{3}$$

To raise \frac{-2}{zx^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-2\right)^{3}}{\left(zx^{4}\right)^{3}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8}{\left(zx^{4}\right)^{3}}$$

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

$$\frac{-8}{z^{3}\left(x^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{-8}{z^{3}x^{12}}$$

Expand

$$-\frac{8}{z^{3}x^{12}}$$

Solution Steps

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

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

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

$$\left(\frac{-2}{zx^{4}}\right)^{3}$$

To raise \frac{-2}{zx^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-2\right)^{3}}{\left(zx^{4}\right)^{3}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8}{\left(zx^{4}\right)^{3}}$$

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

$$\frac{-8}{z^{3}\left(x^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{-8}{z^{3}x^{12}}$$