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

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

Evaluate

$$y^{7}x^{12}$$

Solution Steps

To raise \frac{x^{5}}{y^{-3}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Multiply \frac{\left(x^{5}\right)^{2}}{\left(y^{-3}\right)^{2}} times \frac{\left(x^{-2}\right)^{-1}}{y^{-1}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

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

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

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

$$\frac{x^{12}}{\left(y^{-3}\right)^{2}y^{-1}}$$

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

$$\frac{x^{12}}{y^{-6}y^{-1}}$$

To multiply powers of the same base, add their exponents. Add -6 and -1 to get -7.

$$\frac{x^{12}}{y^{-7}}$$

Expand

$$y^{7}x^{12}$$

Solution Steps

To raise \frac{x^{5}}{y^{-3}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Multiply \frac{\left(x^{5}\right)^{2}}{\left(y^{-3}\right)^{2}} times \frac{\left(x^{-2}\right)^{-1}}{y^{-1}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

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

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

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

$$\frac{x^{12}}{\left(y^{-3}\right)^{2}y^{-1}}$$

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

$$\frac{x^{12}}{y^{-6}y^{-1}}$$

To multiply powers of the same base, add their exponents. Add -6 and -1 to get -7.

$$\frac{x^{12}}{y^{-7}}$$