Solve {left(6y/4div2right)}^2

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

Evaluate

$$\frac{9y^{2}}{16}$$

Solution Steps

Express \frac{\frac{6y}{4}}{2} as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

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

To raise \frac{3y}{4} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{3^{2}y^{2}}{4^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9y^{2}}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9y^{2}}{16}$$

Expand

$$\frac{9y^{2}}{16}$$

Solution Steps

Express \frac{\frac{6y}{4}}{2} as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

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

To raise \frac{3y}{4} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{3^{2}y^{2}}{4^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9y^{2}}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9y^{2}}{16}$$