Solve (frac{x^{4}y^-1}{x^-2y^3})^2

$$( \frac { x ^ { 4 } y ^ { - 1 } } { x ^ { - 2 } y ^ { 3 } } ) ^ { 2 }$$

Evaluate

$$\frac{x^{12}}{y^{8}}$$

Solution Steps

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

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

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

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

To raise \frac{x^{6}}{y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

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

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

$$\frac{x^{12}}{y^{8}}$$

Expand

$$\frac{x^{12}}{y^{8}}$$

Solution Steps

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

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

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

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

To raise \frac{x^{6}}{y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

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

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

$$\frac{x^{12}}{y^{8}}$$