What is 4pi*10^{-7}*80*3 ?

The solution to 4pi*10^{-7}*80*3 is (3pi)/(31250)

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simplify 4pi10^{-7}80*3

simplify

4 π \cdot 1 0^{- 7} \cdot 80 \cdot 3

\frac{3 π}{31250}

Decimal Notation

0.00030 \dots

Solution steps

4 π 1 0^{- 7} \cdot 80 \cdot 3

Apply exponent rule:

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

= 4 \cdot 80 \cdot 3 π \frac{1}{1 0 ^{7}}

Multiply fractions:

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

= \frac{1 \cdot 4 π 80 \cdot 3}{1 0 ^{7}}

Multiply the numbers:

1 \cdot 4 \cdot 80 \cdot 3 = 960

= \frac{960 π}{1 0 ^{7}}

Factor

960 : 2^{6} \cdot 3 \cdot 5

Factor

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

= \frac{2 ^{6} \cdot 3 \cdot 5 π}{2 ^{7} \cdot 5 ^{7}}

Cancel

\frac{2 ^{6} \cdot 3 \cdot 5 π}{2 ^{7} \cdot 5 ^{7}} : \frac{3 π}{5 ^{6} \cdot 2}

= \frac{3 π}{5 ^{6} \cdot 2}

5^{6} \cdot 2 = 31250

= \frac{3 π}{31250}

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