Solve frac{(x^{-5}y^{-2}z^{-4})^2}{x^2y^3z^-3}

$$\frac { ( x ^ { - 5 } y ^ { - 2 } z ^ { - 4 } ) ^ { 2 } } { x ^ { 2 } y ^ { 3 } z ^ { - 3 } }$$

Evaluate

$$\frac{1}{z^{5}y^{7}x^{12}}$$

Solution Steps

Expand \left(x^{-5}y^{-2}z^{-4}\right)^{2}.

$$\frac{\left(x^{-5}\right)^{2}\left(y^{-2}\right)^{2}\left(z^{-4}\right)^{2}}{x^{2}y^{3}z^{-3}}$$

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

$$\frac{x^{-10}\left(y^{-2}\right)^{2}\left(z^{-4}\right)^{2}}{x^{2}y^{3}z^{-3}}$$

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

$$\frac{x^{-10}y^{-4}\left(z^{-4}\right)^{2}}{x^{2}y^{3}z^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 2 to get -8.

$$\frac{x^{-10}y^{-4}z^{-8}}{x^{2}y^{3}z^{-3}}$$

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

$$\frac{1}{z^{5}y^{7}x^{12}}$$

Expand

$$\frac{1}{z^{5}y^{7}x^{12}}$$

Solution Steps

Expand \left(x^{-5}y^{-2}z^{-4}\right)^{2}.

$$\frac{\left(x^{-5}\right)^{2}\left(y^{-2}\right)^{2}\left(z^{-4}\right)^{2}}{x^{2}y^{3}z^{-3}}$$

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

$$\frac{x^{-10}\left(y^{-2}\right)^{2}\left(z^{-4}\right)^{2}}{x^{2}y^{3}z^{-3}}$$

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

$$\frac{x^{-10}y^{-4}\left(z^{-4}\right)^{2}}{x^{2}y^{3}z^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 2 to get -8.

$$\frac{x^{-10}y^{-4}z^{-8}}{x^{2}y^{3}z^{-3}}$$

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

$$\frac{1}{z^{5}y^{7}x^{12}}$$