What is 1000*4pi*10^{-7}*4000^2*0.02^2 ?

The solution to 1000*4pi*10^{-7}*4000^2*0.02^2 is 8.04247…

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simplify 10004pi10^{-7}4000^20.02^2

simplify

1000 \cdot 4 π \cdot 1 0^{- 7} \cdot 400 0^{2} \cdot 0.0 2^{2}

8.04247 \dots

Solution steps

1000 \cdot 4 π 1 0^{- 7} \cdot 400 0^{2} \cdot 0.0 2^{2}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= 400 0^{2} \cdot 1000 \cdot 4 \cdot 0.0 2^{2} π \frac{1}{1 0 ^{7}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 1000 \cdot 4 π 400 0 ^{2} \cdot 0.0 2 ^{2}}{1 0 ^{7}}

1 \cdot 1000 \cdot 4 π 400 0^{2} \cdot 0.0 2^{2} = 400 0^{3} \cdot 0.0 2^{2} π

= \frac{400 0 ^{3} \cdot 0.0 2 ^{2} π}{1 0 ^{7}}

Factor

400 0^{3} : 2^{15} \cdot 5^{9}

Factor

1 0^{7} : 2^{7} \cdot 5^{7}

= \frac{2 ^{15} \cdot 5 ^{9} \cdot 0.0 2 ^{2} π}{2 ^{7} \cdot 5 ^{7}}

Cancel

\frac{π 2 ^{15} \cdot 5 ^{9} \cdot 0.0 2 ^{2}}{2 ^{7} \cdot 5 ^{7}} : 2^{8} \cdot 5^{2} \cdot 0.0 2^{2} π

= 2^{8} \cdot 5^{2} \cdot 0.0 2^{2} π

2^{8} = 256

= 5^{2} \cdot 256 \cdot 0.0 2^{2} π

5^{2} = 25

= 256 \cdot 25 \cdot 0.0 2^{2} π

0.0 2^{2} = 0.0004

= 256 \cdot 25 \cdot 0.0004 π

Multiply the numbers:

256 \cdot 25 \cdot 0.0004 = 2.56

= 2.56 π

Multiply the numbers:

2.56 \cdot 3.14159 \dots = 8.04247 \dots

= 8.04247 \dots

e^{4 x}

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e^{- 30} \frac{1}{1}

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e^{- \frac{3}{4}} \cdot \frac{( \frac{3}{4} ) ^{15}}{15 !}

What is 1000*4pi*10^{-7}*4000^2*0.02^2 ?
The solution to 1000*4pi*10^{-7}*4000^2*0.02^2 is 8.04247…