Solve {left(100/2piright)}^2

$${ \left( \frac{ 100 }{ 2 \pi } \right) }^{ 2 }$$

Evaluate

$$\frac{2500}{\pi ^{2}}\approx 253.302959106$$

Solution Steps

To raise \frac{100}{2\pi } to a power, raise both numerator and denominator to the power and then divide.

$$\frac{100^{2}}{\left(2\pi \right)^{2}}$$

Calculate 100 to the power of 2 and get 10000.

$$\frac{10000}{\left(2\pi \right)^{2}}$$

Expand \left(2\pi \right)^{2}.

$$\frac{10000}{2^{2}\pi ^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{10000}{4\pi ^{2}}$$

Expand

$$\frac{2500}{\pi ^ {2}} = 253.30295910584445$$

Solution Steps

To raise \frac{100}{2\pi } to a power, raise both numerator and denominator to the power and then divide.

$$\frac{100^{2}}{\left(2\pi \right)^{2}}$$

Calculate 100 to the power of 2 and get 10000.

$$\frac{10000}{\left(2\pi \right)^{2}}$$

Expand \left(2\pi \right)^{2}.

$$\frac{10000}{2^{2}\pi ^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{10000}{4\pi ^{2}}$$