What is (160*10^{-6})[1-e^{-500(2*10^{-3})}] ?

The solution to (160*10^{-6})[1-e^{-500(2*10^{-3})}] is (e-1)/(6250e)

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simplify (16010^{-6})[1-e^{-500(210^{-3})}]

simplify

(160 \cdot 1 0^{- 6}) [1 - e^{- 500 (2 \cdot 1 0^{- 3})}]

\frac{e - 1}{6250 e}

Decimal Notation

0.00010 \dots

Solution steps

(160 \cdot 1 0^{- 6}) [1 - e^{- 500 (2 \cdot 1 0^{- 3})}]

Apply exponent rule:

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

= 160 \cdot \frac{1}{1 0 ^{6}} [- e^{- 1 0^{- 3} \cdot 500 \cdot 2} + 1]

Multiply

- 500 \cdot 2 \cdot 1 0^{- 3} : - 1

= 160 \cdot \frac{1}{1 0 ^{6}} (- e^{- 1} + 1)

Multiply fractions:

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

= \frac{1 \cdot 160 ( 1 - e ^{- 1} )}{1 0 ^{6}}

Multiply the numbers:

1 \cdot 160 = 160

= \frac{160 ( - e ^{- 1} + 1 )}{1 0 ^{6}}

Factor

160 : 2^{5} \cdot 5

Factor

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

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

Cancel

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

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

Apply exponent rule:

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

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

Join

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

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

Apply the fraction rule:

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

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

e 5^{5} \cdot 2 = 6250 e

= \frac{e - 1}{6250 e}

1.18 \cdot 1 0^{- 5}

12 (9 - 6 t)^{2} (- 2 - 9 t)^{2} (- 5 - 4 t)

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

(37.3 \cdot 1 0^{- 2}) \cdot (0.01 \cdot 1 0^{2})

c u a d r a d o (a^{m} + a^{n})^{2}

What is (160*10^{-6})[1-e^{-500(2*10^{-3})}] ?
The solution to (160*10^{-6})[1-e^{-500(2*10^{-3})}] is (e-1)/(6250e)