Solve frac{(2x^{-3}y^{-5})^4}{(3x^-2y^-6)^-3}

$$\frac { ( 2 x ^ { - 3 } y ^ { - 5 } ) ^ { 4 } } { ( 3 x ^ { - 2 } y ^ { - 6 } ) ^ { - 3 } }$$

Evaluate

$$\frac{432}{x^{18}y^{38}}$$

Solution Steps

Expand \left(2x^{-3}y^{-5}\right)^{4}.

$$\frac{2^{4}\left(x^{-3}\right)^{4}\left(y^{-5}\right)^{4}}{\left(3x^{-2}y^{-6}\right)^{-3}}$$

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

$$\frac{2^{4}x^{-12}\left(y^{-5}\right)^{4}}{\left(3x^{-2}y^{-6}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -5 and 4 to get -20.

$$\frac{2^{4}x^{-12}y^{-20}}{\left(3x^{-2}y^{-6}\right)^{-3}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16x^{-12}y^{-20}}{\left(3x^{-2}y^{-6}\right)^{-3}}$$

Expand \left(3x^{-2}y^{-6}\right)^{-3}.

$$\frac{16x^{-12}y^{-20}}{3^{-3}\left(x^{-2}\right)^{-3}\left(y^{-6}\right)^{-3}}$$

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

$$\frac{16x^{-12}y^{-20}}{3^{-3}x^{6}\left(y^{-6}\right)^{-3}}$$

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

$$\frac{16x^{-12}y^{-20}}{3^{-3}x^{6}y^{18}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{16x^{-12}y^{-20}}{\frac{1}{27}x^{6}y^{18}}$$

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

$$\frac{16}{\frac{1}{27}x^{18}y^{38}}$$

Expand

$$\frac{432}{x^{18}y^{38}}$$

Solution Steps

Expand \left(2x^{-3}y^{-5}\right)^{4}.

$$\frac{2^{4}\left(x^{-3}\right)^{4}\left(y^{-5}\right)^{4}}{\left(3x^{-2}y^{-6}\right)^{-3}}$$

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

$$\frac{2^{4}x^{-12}\left(y^{-5}\right)^{4}}{\left(3x^{-2}y^{-6}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -5 and 4 to get -20.

$$\frac{2^{4}x^{-12}y^{-20}}{\left(3x^{-2}y^{-6}\right)^{-3}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16x^{-12}y^{-20}}{\left(3x^{-2}y^{-6}\right)^{-3}}$$

Expand \left(3x^{-2}y^{-6}\right)^{-3}.

$$\frac{16x^{-12}y^{-20}}{3^{-3}\left(x^{-2}\right)^{-3}\left(y^{-6}\right)^{-3}}$$

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

$$\frac{16x^{-12}y^{-20}}{3^{-3}x^{6}\left(y^{-6}\right)^{-3}}$$

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

$$\frac{16x^{-12}y^{-20}}{3^{-3}x^{6}y^{18}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{16x^{-12}y^{-20}}{\frac{1}{27}x^{6}y^{18}}$$

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

$$\frac{16}{\frac{1}{27}x^{18}y^{38}}$$