Solve [frac{x^{-2}y^{-1}z^{-4}}{x^4y^-3z^0}]^-3

$$[ \frac { x ^ { - 2 } y ^ { - 1 } z ^ { - 4 } } { x ^ { 4 } y ^ { - 3 } z ^ { 0 } } ] ^ { - 3 }$$

Evaluate

$$\frac{z^{12}x^{18}}{y^{6}}$$

Solution Steps

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

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

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

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

To raise \frac{y^{2}}{z^{4}x^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Expand \left(z^{4}x^{6}\right)^{-3}.

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

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

$$\frac{y^{-6}}{z^{-12}\left(x^{6}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{y^{-6}}{z^{-12}x^{-18}}$$

Expand

$$\frac{z^{12}x^{18}}{y^{6}}$$

Solution Steps

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

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

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

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

To raise \frac{y^{2}}{z^{4}x^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Expand \left(z^{4}x^{6}\right)^{-3}.

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

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

$$\frac{y^{-6}}{z^{-12}\left(x^{6}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{y^{-6}}{z^{-12}x^{-18}}$$