Solve {left(2x^6y^4/5x^7yright)}^2

$${ \left( \frac{ 2 { x }^{ 6 } { y }^{ 4 } }{ 5 { x }^{ 7 } y } \right) }^{ 2 }$$

Evaluate

$$\frac{4y^{6}}{25x^{2}}$$

Solution Steps

Cancel out yx^{6} in both numerator and denominator.

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

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

$$\frac{4y^{6}}{\left(5x\right)^{2}}$$

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

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

Calculate 5 to the power of 2 and get 25.

$$\frac{4y^{6}}{25x^{2}}$$

Expand

$$\frac{4y^{6}}{25x^{2}}$$

Solution Steps

Cancel out yx^{6} in both numerator and denominator.

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

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

$$\frac{4y^{6}}{\left(5x\right)^{2}}$$

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

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

Calculate 5 to the power of 2 and get 25.

$$\frac{4y^{6}}{25x^{2}}$$