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

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

Evaluate

$$\frac{1}{x^{2}z^{6}}$$

Solution Steps

Expand \left(x^{3}y^{-5}z^{2}\right)^{2}.

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

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

$$\frac{x^{6}\left(y^{-5}\right)^{2}\left(z^{2}\right)^{2}}{\left(x^{4}y^{-5}z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}\left(z^{2}\right)^{2}}{\left(x^{4}y^{-5}z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}z^{4}}{\left(x^{4}y^{-5}z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}z^{4}}{\left(x^{4}\right)^{2}\left(y^{-5}\right)^{2}\left(z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}z^{4}}{x^{8}\left(y^{-5}\right)^{2}\left(z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}z^{4}}{x^{8}y^{-10}\left(z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}z^{4}}{x^{8}y^{-10}z^{10}}$$

Cancel out y^{-10}z^{4}x^{6} in both numerator and denominator.

$$\frac{1}{x^{2}z^{6}}$$

Expand

$$\frac{1}{x^{2}z^{6}}$$

Solution Steps

Expand \left(x^{3}y^{-5}z^{2}\right)^{2}.

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

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

$$\frac{x^{6}\left(y^{-5}\right)^{2}\left(z^{2}\right)^{2}}{\left(x^{4}y^{-5}z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}\left(z^{2}\right)^{2}}{\left(x^{4}y^{-5}z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}z^{4}}{\left(x^{4}y^{-5}z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}z^{4}}{\left(x^{4}\right)^{2}\left(y^{-5}\right)^{2}\left(z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}z^{4}}{x^{8}\left(y^{-5}\right)^{2}\left(z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}z^{4}}{x^{8}y^{-10}\left(z^{5}\right)^{2}}$$

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

$$\frac{x^{6}y^{-10}z^{4}}{x^{8}y^{-10}z^{10}}$$

Cancel out y^{-10}z^{4}x^{6} in both numerator and denominator.

$$\frac{1}{x^{2}z^{6}}$$