What is 40*10^{-9}(e^{9.89}-1) ?

The solution to 40*10^{-9}(e^{9.89}-1) is 0.00078…

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simplify 40*10^{-9}(e^{9.89}-1)

simplify

40 \cdot 1 0^{- 9} (e^{9.89} - 1)

0.00078 \dots

Solution steps

40 \cdot 1 0^{- 9} (e^{9.89} - 1)

Apply exponent rule:

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

= 40 \cdot \frac{1}{1 0 ^{9}} (e^{9.89} - 1)

Multiply fractions:

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

= \frac{1 \cdot 40 ( e ^{9.89} - 1 )}{1 0 ^{9}}

Multiply the numbers:

1 \cdot 40 = 40

= \frac{40 ( e ^{9.89} - 1 )}{1 0 ^{9}}

Factor

40 : 2^{3} \cdot 5

Factor

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

= \frac{2 ^{3} \cdot 5 ( e ^{9.89} - 1 )}{2 ^{9} \cdot 5 ^{9}}

Cancel

\frac{2 ^{3} \cdot 5 ( e ^{9.89} - 1 )}{2 ^{9} \cdot 5 ^{9}} : \frac{e ^{9.89} - 1}{5 ^{8} \cdot 2 ^{6}}

= \frac{e ^{9.89} - 1}{5 ^{8} \cdot 2 ^{6}}

e^{9.89} = 19732.05993 \dots

= \frac{19732.05993 \dots - 1}{5 ^{8} \cdot 2 ^{6}}

Subtract the numbers:

19732.05993 \dots - 1 = 19731.05993 \dots

= \frac{19731.05993 \dots}{5 ^{8} \cdot 2 ^{6}}

5^{8} \cdot 2^{6} = 25000000

= \frac{19731.05993 \dots}{25000000}

Divide the numbers:

\frac{19731.05993 \dots}{25000000} = 0.00078 \dots

= 0.00078 \dots

2.25 \cdot e^{- 12}

\frac{e ^{- k t}}{e ^{j t}}

e^{- 3.16746}

[(- 3)^{- 2}]^{\frac{1}{2}}

(x - 2)^{2} (y - 4)^{2} 36

What is 40*10^{-9}(e^{9.89}-1) ?
The solution to 40*10^{-9}(e^{9.89}-1) is 0.00078…