Solve 1/2{left(x/2*1/2right)}^2pi

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

Evaluate

$$\frac{\pi x^{2}}{32}$$

Solution Steps

Multiply \frac{x}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply \frac{1}{2} times \frac{x^{2}}{\left(2\times 2\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Express \frac{x^{2}}{2\times \left(2\times 2\right)^{2}}\pi as a single fraction.

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

Multiply 2 and 2 to get 4.

$$\frac{x^{2}\pi }{2\times 4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{x^{2}\pi }{2\times 16}$$

Multiply 2 and 16 to get 32.

$$\frac{x^{2}\pi }{32}$$

Expand

$$\frac{\pi x^{2}}{32}$$

Solution Steps

Multiply \frac{x}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply \frac{1}{2} times \frac{x^{2}}{\left(2\times 2\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Express \frac{x^{2}}{2\times \left(2\times 2\right)^{2}}\pi as a single fraction.

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

Multiply 2 and 2 to get 4.

$$\frac{x^{2}\pi }{2\times 4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{x^{2}\pi }{2\times 16}$$

Multiply 2 and 16 to get 32.

$$\frac{x^{2}\pi }{32}$$