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

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

Evaluate

$$\frac{4}{25y^{4}x^{6}}$$

Solution Steps

Cancel out x^{3}y^{3} in both numerator and denominator.

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

To raise \frac{2}{5y^{2}x^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

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

$$\frac{4}{5^{2}y^{4}x^{6}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{4}{25y^{4}x^{6}}$$

Expand

$$\frac{4}{25y^{4}x^{6}}$$

Solution Steps

Cancel out x^{3}y^{3} in both numerator and denominator.

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

To raise \frac{2}{5y^{2}x^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

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

$$\frac{4}{5^{2}y^{4}x^{6}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{4}{25y^{4}x^{6}}$$