What is 4pi*10^{-7}*300*10 ?

The solution to 4pi*10^{-7}*300*10 is (3pi)/(2500)

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simplify 4pi10^{-7}300*10

simplify

4 π \cdot 1 0^{- 7} \cdot 300 \cdot 10

\frac{3 π}{2500}

Decimal Notation

0.00376 \dots

Solution steps

4 π 1 0^{- 7} \cdot 300 \cdot 10

Apply exponent rule:

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

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

= 4 π 300 \cdot 1 0^{- 7 + 1}

Add/Subtract the numbers:

- 7 + 1 = - 6

= 4 π 300 \cdot 1 0^{- 6}

Apply exponent rule:

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

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

= 4 \cdot 300 π \frac{1}{1 0 ^{6}}

Multiply fractions:

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

= \frac{1 \cdot 4 π 300}{1 0 ^{6}}

Multiply the numbers:

1 \cdot 4 \cdot 300 = 1200

= \frac{1200 π}{1 0 ^{6}}

Factor

1200 : 2^{4} \cdot 5^{2} \cdot 3

Factor

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

= \frac{2 ^{4} \cdot 5 ^{2} \cdot 3 π}{2 ^{6} \cdot 5 ^{6}}

Cancel

\frac{2 ^{4} \cdot 3 \cdot 5 ^{2} π}{2 ^{6} \cdot 5 ^{6}} : \frac{3 π}{5 ^{4} \cdot 2 ^{2}}

= \frac{3 π}{5 ^{4} \cdot 2 ^{2}}

5^{4} \cdot 2^{2} = 2500

= \frac{3 π}{2500}

20 e^{- 500 (t - 10)} u (t - 10)

- \frac{18}{12}

(3 + x)^{- 2}

(4.9 \cdot 1 0^{3}) \cdot (7.4 \cdot 1 0^{- 6})