Solve 1.28*10^-4/pi*left(8.50*10^-2right)^2*385*4pi*10^-7

$$\frac{ 1.28 \times { 10 }^{ -4 } }{ \pi \times { \left(8.50 \times { 10 }^{ -2 } \right) }^{ 2 } \times 385 \cdot 4 \pi \times { 10 }^{ -7 } }$$

Evaluate

$$\frac{2560000}{22253\pi ^{2}}\approx 11.656056717$$

Solution Steps

Multiply \pi and \pi to get \pi ^{2}.

$$\frac{1.28\times 10^{-4}}{\pi ^{2}\times \left(8.5\times 10^{-2}\right)^{2}\times 385\times 4\times 10^{-7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{1.28\times 10^{3}}{4\times 385\pi ^{2}\times \left(8.5\times 10^{-2}\right)^{2}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{1.28\times 1000}{4\times 385\pi ^{2}\times \left(8.5\times 10^{-2}\right)^{2}}$$

Multiply 1.28 and 1000 to get 1280.

$$\frac{1280}{4\times 385\pi ^{2}\times \left(8.5\times 10^{-2}\right)^{2}}$$

Multiply 4 and 385 to get 1540.

$$\frac{1280}{1540\pi ^{2}\times \left(8.5\times 10^{-2}\right)^{2}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{1280}{1540\pi ^{2}\times \left(8.5\times \frac{1}{100}\right)^{2}}$$

Multiply 8.5 and \frac{1}{100} to get \frac{17}{200}.

$$\frac{1280}{1540\pi ^{2}\times \left(\frac{17}{200}\right)^{2}}$$

Calculate \frac{17}{200} to the power of 2 and get \frac{289}{40000}.

$$\frac{1280}{1540\pi ^{2}\times \frac{289}{40000}}$$

Multiply 1540 and \frac{289}{40000} to get \frac{22253}{2000}.

$$\frac{1280}{\frac{22253}{2000}\pi ^{2}}$$

Expand

$$\frac{2560000}{22253 \pi ^ {2}} = 11.656056717044207$$

Solution Steps

Multiply \pi and \pi to get \pi ^{2}.

$$\frac{1.28\times 10^{-4}}{\pi ^{2}\times \left(8.5\times 10^{-2}\right)^{2}\times 385\times 4\times 10^{-7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{1.28\times 10^{3}}{4\times 385\pi ^{2}\times \left(8.5\times 10^{-2}\right)^{2}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{1.28\times 1000}{4\times 385\pi ^{2}\times \left(8.5\times 10^{-2}\right)^{2}}$$

Multiply 1.28 and 1000 to get 1280.

$$\frac{1280}{4\times 385\pi ^{2}\times \left(8.5\times 10^{-2}\right)^{2}}$$

Multiply 4 and 385 to get 1540.

$$\frac{1280}{1540\pi ^{2}\times \left(8.5\times 10^{-2}\right)^{2}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{1280}{1540\pi ^{2}\times \left(8.5\times \frac{1}{100}\right)^{2}}$$

Multiply 8.5 and \frac{1}{100} to get \frac{17}{200}.

$$\frac{1280}{1540\pi ^{2}\times \left(\frac{17}{200}\right)^{2}}$$

Calculate \frac{17}{200} to the power of 2 and get \frac{289}{40000}.

$$\frac{1280}{1540\pi ^{2}\times \frac{289}{40000}}$$

Multiply 1540 and \frac{289}{40000} to get \frac{22253}{2000}.

$$\frac{1280}{\frac{22253}{2000}\pi ^{2}}$$