Solve (x^{-2}y)^-5*(x^3/y^2)^-4

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

Evaluate

$$\frac{y^{3}}{x^{2}}$$

Solution Steps

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

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

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

$$x^{10}y^{-5}\times \left(\frac{x^{3}}{y^{2}}\right)^{-4}$$

To raise \frac{x^{3}}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$x^{10}y^{-5}\times \frac{\left(x^{3}\right)^{-4}}{\left(y^{2}\right)^{-4}}$$

Express x^{10}\times \frac{\left(x^{3}\right)^{-4}}{\left(y^{2}\right)^{-4}} as a single fraction.

$$\frac{x^{10}\left(x^{3}\right)^{-4}}{\left(y^{2}\right)^{-4}}y^{-5}$$

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

$$\frac{x^{10}x^{-12}}{\left(y^{2}\right)^{-4}}y^{-5}$$

To multiply powers of the same base, add their exponents. Add 10 and -12 to get -2.

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

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

$$\frac{x^{-2}}{y^{-8}}y^{-5}$$

Express \frac{x^{-2}}{y^{-8}}y^{-5} as a single fraction.

$$\frac{x^{-2}y^{-5}}{y^{-8}}$$

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

$$x^{-2}y^{3}$$

Expand

$$\frac{y^{3}}{x^{2}}$$

Solution Steps

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

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

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

$$x^{10}y^{-5}\times \left(\frac{x^{3}}{y^{2}}\right)^{-4}$$

To raise \frac{x^{3}}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$x^{10}y^{-5}\times \frac{\left(x^{3}\right)^{-4}}{\left(y^{2}\right)^{-4}}$$

Express x^{10}\times \frac{\left(x^{3}\right)^{-4}}{\left(y^{2}\right)^{-4}} as a single fraction.

$$\frac{x^{10}\left(x^{3}\right)^{-4}}{\left(y^{2}\right)^{-4}}y^{-5}$$

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

$$\frac{x^{10}x^{-12}}{\left(y^{2}\right)^{-4}}y^{-5}$$

To multiply powers of the same base, add their exponents. Add 10 and -12 to get -2.

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

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

$$\frac{x^{-2}}{y^{-8}}y^{-5}$$

Express \frac{x^{-2}}{y^{-8}}y^{-5} as a single fraction.

$$\frac{x^{-2}y^{-5}}{y^{-8}}$$

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

$$x^{-2}y^{3}$$