What is 4pi*10^{-7}*(1000)/(0.2)*10 ?

The solution to 4pi*10^{-7}*(1000)/(0.2)*10 is pi/(50)

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simplify 4pi10^{-7}(1000)/(0.2)*10

simplify

4 π \cdot 1 0^{- 7} \cdot \frac{1000}{0.2} \cdot 10

\frac{π}{50}

Decimal Notation

0.06283 \dots

Solution steps

4 π 1 0^{- 7} \cdot \frac{1000}{0.2} \cdot 10

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

1 0^{- 7} \cdot 10 = 1 0^{- 7 + 1}

= 4 π \frac{1000}{0.2} \cdot 1 0^{- 7 + 1}

Add/Subtract the numbers:

- 7 + 1 = - 6

= 4 π \frac{1000}{0.2} \cdot 1 0^{- 6}

Apply exponent rule:

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

1 0^{- 6} = \frac{1}{1 0 ^{6}}

= 4 π \frac{1000}{0.2} \cdot \frac{1}{1 0 ^{6}}

Multiply fractions:

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

= \frac{1000 \cdot 1 \cdot 4 π}{0.2 \cdot 1 0 ^{6}}

Multiply the numbers:

1000 \cdot 1 \cdot 4 = 4000

= \frac{4000 π}{1 0 ^{6} \cdot 0.2}

Factor

4000 : 2^{5} \cdot 5^{3}

Factor

1 0^{6} : 2^{6} \cdot 5^{6}

= \frac{2 ^{5} \cdot 5 ^{3} π}{2 ^{6} \cdot 5 ^{6} \cdot 0.2}

Cancel

\frac{2 ^{5} \cdot 5 ^{3} π}{0.2 \cdot 2 ^{6} \cdot 5 ^{6}} : \frac{π}{5 ^{3} \cdot 2 \cdot 0.2}

= \frac{π}{5 ^{3} \cdot 2 \cdot 0.2}

Multiply the numbers:

2 \cdot 0.2 = 0.4

= \frac{π}{5 ^{3} \cdot 0.4}

0.4 \cdot 5^{3} = 50

= \frac{π}{50}

7.29 \cdot 1 0^{- 5}

t e^{- 3 t} cos (x)

1.26 x 1 0^{- 2} \cdot 74.092

(a - b)^{3} (a + b)^{3}

e^{- 2 t} cos (h) (3 t)

What is 4pi*10^{-7}*(1000)/(0.2)*10 ?
The solution to 4pi*10^{-7}*(1000)/(0.2)*10 is pi/(50)