Solve =frac{pi^{2}*200*10^9*1/64*7*(60*10^-3)^4}{(0.5*4sqrt{2})^2}

$$= \frac { \pi ^ { 2 } \times 200 \times 10 ^ { 9 } \times \frac { 1 } { 64 } \times 7 \times ( 60 \times 10 ^ { - 3 } ) ^ { 4 } } { ( 0.5 \times 4 \sqrt { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{70875\pi ^{2}}{2}\approx 349754.105963604$$

Solution Steps

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\pi ^{2}\times 200\times 1000000000\times \frac{1}{64}\times 7\times \left(60\times 10^{-3}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 200 and 1000000000 to get 200000000000.

$$\frac{\pi ^{2}\times 200000000000\times \frac{1}{64}\times 7\times \left(60\times 10^{-3}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 200000000000 and \frac{1}{64} to get 3125000000.

$$\frac{\pi ^{2}\times 3125000000\times 7\times \left(60\times 10^{-3}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 3125000000 and 7 to get 21875000000.

$$\frac{\pi ^{2}\times 21875000000\times \left(60\times 10^{-3}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{\pi ^{2}\times 21875000000\times \left(60\times \frac{1}{1000}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 60 and \frac{1}{1000} to get \frac{3}{50}.

$$\frac{\pi ^{2}\times 21875000000\times \left(\frac{3}{50}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Calculate \frac{3}{50} to the power of 4 and get \frac{81}{6250000}.

$$\frac{\pi ^{2}\times 21875000000\times \frac{81}{6250000}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 21875000000 and \frac{81}{6250000} to get 283500.

$$\frac{\pi ^{2}\times 283500}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 0.5 and 4 to get 2.

$$\frac{\pi ^{2}\times 283500}{\left(2\sqrt{2}\right)^{2}}$$

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

$$\frac{\pi ^{2}\times 283500}{2^{2}\left(\sqrt{2}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\pi ^{2}\times 283500}{4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\pi ^{2}\times 283500}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{\pi ^{2}\times 283500}{8}$$

Divide \pi ^{2}\times 283500 by 8 to get \pi ^{2}\times \frac{70875}{2}.

$$\pi ^{2}\times \frac{70875}{2}$$

Expand

$$\frac{70875 \pi ^ {2}}{2} = 349754.1059636041$$

Solution Steps

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\pi ^{2}\times 200\times 1000000000\times \frac{1}{64}\times 7\times \left(60\times 10^{-3}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 200 and 1000000000 to get 200000000000.

$$\frac{\pi ^{2}\times 200000000000\times \frac{1}{64}\times 7\times \left(60\times 10^{-3}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 200000000000 and \frac{1}{64} to get 3125000000.

$$\frac{\pi ^{2}\times 3125000000\times 7\times \left(60\times 10^{-3}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 3125000000 and 7 to get 21875000000.

$$\frac{\pi ^{2}\times 21875000000\times \left(60\times 10^{-3}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{\pi ^{2}\times 21875000000\times \left(60\times \frac{1}{1000}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 60 and \frac{1}{1000} to get \frac{3}{50}.

$$\frac{\pi ^{2}\times 21875000000\times \left(\frac{3}{50}\right)^{4}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Calculate \frac{3}{50} to the power of 4 and get \frac{81}{6250000}.

$$\frac{\pi ^{2}\times 21875000000\times \frac{81}{6250000}}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 21875000000 and \frac{81}{6250000} to get 283500.

$$\frac{\pi ^{2}\times 283500}{\left(0.5\times 4\sqrt{2}\right)^{2}}$$

Multiply 0.5 and 4 to get 2.

$$\frac{\pi ^{2}\times 283500}{\left(2\sqrt{2}\right)^{2}}$$

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

$$\frac{\pi ^{2}\times 283500}{2^{2}\left(\sqrt{2}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\pi ^{2}\times 283500}{4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\pi ^{2}\times 283500}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{\pi ^{2}\times 283500}{8}$$

Divide \pi ^{2}\times 283500 by 8 to get \pi ^{2}\times \frac{70875}{2}.

$$\pi ^{2}\times \frac{70875}{2}$$