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

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

Evaluate

$$\frac{x^{2}}{y^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

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

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

$$\left(\frac{x^{1}y^{4}}{y^{6}}\right)^{2}$$

Cancel out y^{4} in both numerator and denominator.

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

Calculate x to the power of 1 and get x.

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

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

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

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

$$\frac{x^{2}}{y^{4}}$$

Expand

$$\frac{x^{2}}{y^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

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

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

$$\left(\frac{x^{1}y^{4}}{y^{6}}\right)^{2}$$

Cancel out y^{4} in both numerator and denominator.

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

Calculate x to the power of 1 and get x.

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

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

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

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

$$\frac{x^{2}}{y^{4}}$$