What is 4pi*10^{-7}*20*400 ?

The solution to 4pi*10^{-7}*20*400 is (2pi)/(625)

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simplify 4pi10^{-7}20*400

simplify

4 π \cdot 1 0^{- 7} \cdot 20 \cdot 400

\frac{2 π}{625}

Solution steps

4 π 1 0^{- 7} \cdot 20 \cdot 400

Apply exponent rule:

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

= 4 \cdot 20 \cdot 400 π \frac{1}{1 0 ^{7}}

Multiply fractions:

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

= \frac{1 \cdot 4 π 20 \cdot 400}{1 0 ^{7}}

Multiply the numbers:

1 \cdot 4 \cdot 20 \cdot 400 = 32000

= \frac{32000 π}{1 0 ^{7}}

Factor

32000 : 2^{8} \cdot 5^{3}

Factor

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

= \frac{2 ^{8} \cdot 5 ^{3} π}{2 ^{7} \cdot 5 ^{7}}

Cancel

\frac{2 ^{8} \cdot 5 ^{3} π}{2 ^{7} \cdot 5 ^{7}} : \frac{2 π}{5 ^{4}}

= \frac{2 π}{5 ^{4}}

5^{4} = 625

= \frac{2 π}{625}

(1 - e^{x}) (1 - e^{x})

a b \cdot b a

24 x^{3} y^{3}

16 e^{- 0.2 (1)}

3^{\frac{1}{2}}