What is 18*10^{-9}*1/(2*pi*8.85*10^{-12)*0.03} ?

The solution to 18*10^{-9}*1/(2*pi*8.85*10^{-12)*0.03} is 10790.16563…

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simplify 1810^{-9}1/(2pi8.8510^{-12)0.03}

simplify

18 \cdot 1 0^{- 9} \cdot \frac{1}{2 \cdot π \cdot 8.85 \cdot 1 0 ^{- 12} \cdot 0.03}

10790.16563 \dots

Solution steps

18 \cdot 1 0^{- 9} \cdot \frac{1}{2 π 8.85 \cdot 1 0 ^{- 12} \cdot 0.03}

Apply exponent rule:

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

= 18 \cdot \frac{1}{1 0 ^{9}} \cdot \frac{1}{1 0 ^{- 12} \cdot 2 \cdot 0.03 \cdot 8.85 π}

\frac{1}{2 π 8.85 \cdot 1 0 ^{- 12} \cdot 0.03} = \frac{1}{1.66819 E - 12}

= 18 \cdot \frac{1}{1 0 ^{9}} \cdot \frac{1}{1.66819 E - 12}

Multiply fractions:

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

= \frac{1 \cdot 1 \cdot 18}{1 0 ^{9} \cdot 1.66819 E - 12}

Multiply the numbers:

1 \cdot 1 \cdot 18 = 18

= \frac{18}{1 0 ^{9} \cdot 1.66819 E - 12}

Factor

18 : 3^{2} \cdot 2

Factor

1 0^{9} : 2^{9} \cdot 5^{9}

= \frac{3 ^{2} \cdot 2}{2 ^{9} \cdot 5 ^{9} \cdot 1.66819 E - 12}

Cancel the common factor:

2

= \frac{3 ^{2}}{5 ^{9} \cdot 2 ^{8} \cdot 1.66819 E - 12}

3^{2} = 9

= \frac{9}{5 ^{9} \cdot 2 ^{8} \cdot 1.66819 E - 12}

5^{9} \cdot 2^{8} \cdot 1.66819 E - 12 = 0.00083 \dots

= \frac{9}{0.00083 \dots}

Divide the numbers:

\frac{9}{0.00083 \dots} = 10790.16563 \dots

= 10790.16563 \dots

(e^{- 2 x}) (e^{3 x})

e^{- 0.066}

s^{2} (s^{2} + 2)^{2}

What is 18*10^{-9}*1/(2*pi*8.85*10^{-12)*0.03} ?
The solution to 18*10^{-9}*1/(2*pi*8.85*10^{-12)*0.03} is 10790.16563…