What is (4*10^{-6})*(1-e^{-1/3}) ?

The solution to (4*10^{-6})*(1-e^{-1/3}) is (e^{1/3}-1)/(250000e^{1/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (410^{-6})(1-e^{-1/3})

simplify

(4 \cdot 1 0^{- 6}) \cdot (1 - e^{- \frac{1}{3}})

\frac{e ^{\frac{1}{3}} - 1}{250000 e ^{\frac{1}{3}}}

Decimal Notation

1.13387 E - 6

Solution steps

(4 \cdot 1 0^{- 6}) (1 - e^{- \frac{1}{3}})

Apply exponent rule:

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

= 4 \cdot \frac{1}{1 0 ^{6}} (- e^{- \frac{1}{3}} + 1)

Multiply fractions:

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

= \frac{1 \cdot 4 ( 1 - e ^{- \frac{1}{3}} )}{1 0 ^{6}}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4 ( - e ^{- \frac{1}{3}} + 1 )}{1 0 ^{6}}

Factor

4 : 2^{2}

Factor

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

= \frac{2 ^{2} ( - e ^{- \frac{1}{3}} + 1 )}{2 ^{6} \cdot 5 ^{6}}

Cancel

\frac{2 ^{2} ( 1 - e ^{- \frac{1}{3}} )}{2 ^{6} \cdot 5 ^{6}} : \frac{1 - e ^{- \frac{1}{3}}}{5 ^{6} \cdot 2 ^{4}}

= \frac{1 - e ^{- \frac{1}{3}}}{5 ^{6} \cdot 2 ^{4}}

Apply exponent rule:

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

= \frac{1 - \frac{1}{e ^{\frac{1}{3}}}}{5 ^{6} \cdot 2 ^{4}}

Join

1 - \frac{1}{e ^{\frac{1}{3}}} : \frac{e ^{\frac{1}{3}} - 1}{e ^{\frac{1}{3}}}

= \frac{\frac{e ^{\frac{1}{3}} - 1}{e ^{\frac{1}{3}}}}{5 ^{6} \cdot 2 ^{4}}

Apply the fraction rule:

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

= \frac{e ^{\frac{1}{3}} - 1}{e ^{\frac{1}{3}} \cdot 5 ^{6} \cdot 2 ^{4}}

e^{\frac{1}{3}} \cdot 5^{6} \cdot 2^{4} = 250000 e^{\frac{1}{3}}

= \frac{e ^{\frac{1}{3}} - 1}{250000 e ^{\frac{1}{3}}}

\frac{( 2 π α _{1} ) ^{- \frac{n}{2}}}{( 2 π α _{2} ) ^{- \frac{n}{2}}}

e^{- t} sin (x)

(3 x^{4} y^{5} z) (2 x^{2} y^{8} z^{2})

4.85 x 1 0^{- 4}

\frac{1}{3} (e^{3 t} - 1)^{2} e^{- 5 t}

What is (4*10^{-6})*(1-e^{-1/3}) ?
The solution to (4*10^{-6})*(1-e^{-1/3}) is (e^{1/3}-1)/(250000e^{1/3)}