Solve (6.62*10^-34)^2/8*frac{4*64{6.02*10^3}}*[3/pi*4/47.04*10^-35]

$$\frac { ( 6.62 \times 10 ^ { - 34 } ) ^ { 2 } } { 8 \times \frac { 4 \times 64 } { 6.02 \times 10 ^ { 3 } } } \times [ \frac { 3 } { \pi } \times \frac { 4 } { 47.04 \times 10 ^ { - 35 } } ]$$

Evaluate

$$\frac{4711123}{143360000000000000000000000000000000000\pi }\approx 1.046035872 \cdot 10^{-32}$$

Solution Steps

Calculate 10 to the power of -34 and get \frac{1}{10000000000000000000000000000000000}.

$$\frac{\left(6.62\times \frac{1}{10000000000000000000000000000000000}\right)^{2}}{8\times \frac{4\times 64}{6.02\times 10^{3}}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Multiply 6.62 and \frac{1}{10000000000000000000000000000000000} to get \frac{331}{500000000000000000000000000000000000}.

$$\frac{\left(\frac{331}{500000000000000000000000000000000000}\right)^{2}}{8\times \frac{4\times 64}{6.02\times 10^{3}}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Calculate \frac{331}{500000000000000000000000000000000000} to the power of 2 and get \frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{8\times \frac{4\times 64}{6.02\times 10^{3}}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Multiply 4 and 64 to get 256.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{8\times \frac{256}{6.02\times 10^{3}}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{8\times \frac{256}{6.02\times 1000}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Multiply 6.02 and 1000 to get 6020.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{8\times \frac{256}{6020}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Reduce the fraction \frac{256}{6020} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{8\times \frac{64}{1505}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Multiply 8 and \frac{64}{1505} to get \frac{512}{1505}.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{512}{1505}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Divide \frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000} by \frac{512}{1505} by multiplying \frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000} by the reciprocal of \frac{512}{1505}.

$$\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{1505}{512}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Multiply \frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000} and \frac{1505}{512} to get \frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Calculate 10 to the power of -35 and get \frac{1}{100000000000000000000000000000000000}.

$$\frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{3}{\pi }\times \frac{4}{47.04\times \frac{1}{100000000000000000000000000000000000}}$$

Multiply 47.04 and \frac{1}{100000000000000000000000000000000000} to get \frac{147}{312500000000000000000000000000000000}.

$$\frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{3}{\pi }\times \frac{4}{\frac{147}{312500000000000000000000000000000000}}$$

Divide 4 by \frac{147}{312500000000000000000000000000000000} by multiplying 4 by the reciprocal of \frac{147}{312500000000000000000000000000000000}.

$$\frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{3}{\pi }\times 4\times \frac{312500000000000000000000000000000000}{147}$$

Multiply 4 and \frac{312500000000000000000000000000000000}{147} to get \frac{1250000000000000000000000000000000000}{147}.

$$\frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{3}{\pi }\times \frac{1250000000000000000000000000000000000}{147}$$

Multiply \frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000} and \frac{1250000000000000000000000000000000000}{147} to get \frac{4711123}{430080000000000000000000000000000000000}.

$$\frac{4711123}{430080000000000000000000000000000000000}\times \frac{3}{\pi }$$

Multiply \frac{4711123}{430080000000000000000000000000000000000} times \frac{3}{\pi } by multiplying numerator times numerator and denominator times denominator.

$$\frac{4711123\times 3}{430080000000000000000000000000000000000\pi }$$

Cancel out 3 in both numerator and denominator.

$$\frac{4711123}{143360000000000000000000000000000000000\pi }$$

Expand

$$\frac{4711123}{143360000000000000000000000000000000000 \pi} = 1.0460358718804676 \times 10^{-32}$$

Solution Steps

Calculate 10 to the power of -34 and get \frac{1}{10000000000000000000000000000000000}.

$$\frac{\left(6.62\times \frac{1}{10000000000000000000000000000000000}\right)^{2}}{8\times \frac{4\times 64}{6.02\times 10^{3}}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Multiply 6.62 and \frac{1}{10000000000000000000000000000000000} to get \frac{331}{500000000000000000000000000000000000}.

$$\frac{\left(\frac{331}{500000000000000000000000000000000000}\right)^{2}}{8\times \frac{4\times 64}{6.02\times 10^{3}}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Calculate \frac{331}{500000000000000000000000000000000000} to the power of 2 and get \frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{8\times \frac{4\times 64}{6.02\times 10^{3}}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Multiply 4 and 64 to get 256.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{8\times \frac{256}{6.02\times 10^{3}}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{8\times \frac{256}{6.02\times 1000}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Multiply 6.02 and 1000 to get 6020.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{8\times \frac{256}{6020}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Reduce the fraction \frac{256}{6020} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{8\times \frac{64}{1505}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Multiply 8 and \frac{64}{1505} to get \frac{512}{1505}.

$$\frac{\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{512}{1505}}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Divide \frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000} by \frac{512}{1505} by multiplying \frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000} by the reciprocal of \frac{512}{1505}.

$$\frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{1505}{512}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Multiply \frac{109561}{250000000000000000000000000000000000000000000000000000000000000000000000} and \frac{1505}{512} to get \frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{3}{\pi }\times \frac{4}{47.04\times 10^{-35}}$$

Calculate 10 to the power of -35 and get \frac{1}{100000000000000000000000000000000000}.

$$\frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{3}{\pi }\times \frac{4}{47.04\times \frac{1}{100000000000000000000000000000000000}}$$

Multiply 47.04 and \frac{1}{100000000000000000000000000000000000} to get \frac{147}{312500000000000000000000000000000000}.

$$\frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{3}{\pi }\times \frac{4}{\frac{147}{312500000000000000000000000000000000}}$$

Divide 4 by \frac{147}{312500000000000000000000000000000000} by multiplying 4 by the reciprocal of \frac{147}{312500000000000000000000000000000000}.

$$\frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{3}{\pi }\times 4\times \frac{312500000000000000000000000000000000}{147}$$

Multiply 4 and \frac{312500000000000000000000000000000000}{147} to get \frac{1250000000000000000000000000000000000}{147}.

$$\frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{3}{\pi }\times \frac{1250000000000000000000000000000000000}{147}$$

Multiply \frac{32977861}{25600000000000000000000000000000000000000000000000000000000000000000000000} and \frac{1250000000000000000000000000000000000}{147} to get \frac{4711123}{430080000000000000000000000000000000000}.

$$\frac{4711123}{430080000000000000000000000000000000000}\times \frac{3}{\pi }$$

Multiply \frac{4711123}{430080000000000000000000000000000000000} times \frac{3}{\pi } by multiplying numerator times numerator and denominator times denominator.

$$\frac{4711123\times 3}{430080000000000000000000000000000000000\pi }$$

Cancel out 3 in both numerator and denominator.

$$\frac{4711123}{143360000000000000000000000000000000000\pi }$$