Solve frac{(3x^{3}y^{5})^{-2}}{(x^2y^2z^2)^-1}=

$$\frac { ( 3 x ^ { 3 } y ^ { 5 } ) ^ { - 2 } } { ( x ^ { 2 } y ^ { 2 } z ^ { 2 } ) ^ { - 1 } } =$$

Evaluate

$$\frac{z^{2}}{9x^{4}y^{8}}$$

Solution Steps

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

$$\frac{3^{-2}\left(x^{3}\right)^{-2}\left(y^{5}\right)^{-2}}{\left(x^{2}y^{2}z^{2}\right)^{-1}}$$

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

$$\frac{3^{-2}x^{-6}\left(y^{5}\right)^{-2}}{\left(x^{2}y^{2}z^{2}\right)^{-1}}$$

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

$$\frac{3^{-2}x^{-6}y^{-10}}{\left(x^{2}y^{2}z^{2}\right)^{-1}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}x^{-6}y^{-10}}{\left(x^{2}y^{2}z^{2}\right)^{-1}}$$

Expand \left(x^{2}y^{2}z^{2}\right)^{-1}.

$$\frac{\frac{1}{9}x^{-6}y^{-10}}{\left(x^{2}\right)^{-1}\left(y^{2}\right)^{-1}\left(z^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\frac{1}{9}x^{-6}y^{-10}}{x^{-2}\left(y^{2}\right)^{-1}\left(z^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\frac{1}{9}x^{-6}y^{-10}}{x^{-2}y^{-2}\left(z^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\frac{1}{9}x^{-6}y^{-10}}{x^{-2}y^{-2}z^{-2}}$$

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

$$\frac{\frac{1}{9}}{z^{-2}x^{4}y^{8}}$$

Express \frac{\frac{1}{9}}{z^{-2}x^{4}y^{8}} as a single fraction.

$$\frac{1}{9z^{-2}x^{4}y^{8}}$$

Expand

$$\frac{z^{2}}{9x^{4}y^{8}}$$

Solution Steps

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

$$\frac{3^{-2}\left(x^{3}\right)^{-2}\left(y^{5}\right)^{-2}}{\left(x^{2}y^{2}z^{2}\right)^{-1}}$$

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

$$\frac{3^{-2}x^{-6}\left(y^{5}\right)^{-2}}{\left(x^{2}y^{2}z^{2}\right)^{-1}}$$

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

$$\frac{3^{-2}x^{-6}y^{-10}}{\left(x^{2}y^{2}z^{2}\right)^{-1}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}x^{-6}y^{-10}}{\left(x^{2}y^{2}z^{2}\right)^{-1}}$$

Expand \left(x^{2}y^{2}z^{2}\right)^{-1}.

$$\frac{\frac{1}{9}x^{-6}y^{-10}}{\left(x^{2}\right)^{-1}\left(y^{2}\right)^{-1}\left(z^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\frac{1}{9}x^{-6}y^{-10}}{x^{-2}\left(y^{2}\right)^{-1}\left(z^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\frac{1}{9}x^{-6}y^{-10}}{x^{-2}y^{-2}\left(z^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\frac{1}{9}x^{-6}y^{-10}}{x^{-2}y^{-2}z^{-2}}$$

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

$$\frac{\frac{1}{9}}{z^{-2}x^{4}y^{8}}$$

Express \frac{\frac{1}{9}}{z^{-2}x^{4}y^{8}} as a single fraction.

$$\frac{1}{9z^{-2}x^{4}y^{8}}$$