What is 2*3*10^{-4}*e^{-1/10}*10^{-2} ?

The solution to 2*3*10^{-4}*e^{-1/10}*10^{-2} is 3/(500000e^{1/10)}

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simplify 2310^{-4}e^{-1/10}10^{-2}

simplify

2 \cdot 3 \cdot 1 0^{- 4} \cdot e^{- \frac{1}{10}} \cdot 1 0^{- 2}

\frac{3}{500000 e ^{\frac{1}{10}}}

Solution steps

2 \cdot 3 \cdot 1 0^{- 4} e^{- \frac{1}{10}} \cdot 1 0^{- 2}

Apply exponent rule:

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

1 0^{- 4} \cdot 1 0^{- 2} = 1 0^{- 4 - 2}

= 2 \cdot 3 e^{- \frac{1}{10}} \cdot 1 0^{- 4 - 2}

Subtract the numbers:

- 4 - 2 = - 6

= 2 \cdot 3 e^{- \frac{1}{10}} \cdot 1 0^{- 6}

Apply exponent rule:

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

e^{- \frac{1}{10}} = \frac{1}{e ^{\frac{1}{10}}}

= 1 0^{- 6} \cdot 2 \cdot 3 \cdot \frac{1}{e ^{\frac{1}{10}}}

Apply exponent rule:

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

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

= 2 \cdot 3 \cdot \frac{1}{1 0 ^{6}} \cdot \frac{1}{e ^{\frac{1}{10}}}

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 2 \cdot 3}{e ^{\frac{1}{10}} \cdot 1 0 ^{6}}

Multiply the numbers:

1 \cdot 1 \cdot 2 \cdot 3 = 6

= \frac{6}{1 0 ^{6} e ^{\frac{1}{10}}}

Factor

6 : 2 \cdot 3

Factor

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

= \frac{2 \cdot 3}{2 ^{6} \cdot 5 ^{6} e ^{\frac{1}{10}}}

Cancel the common factor:

2

= \frac{3}{5 ^{6} \cdot 2 ^{5} e ^{\frac{1}{10}}}

5^{6} \cdot 2^{5} e^{\frac{1}{10}} = 500000 e^{\frac{1}{10}}

= \frac{3}{500000 e ^{\frac{1}{10}}}

e^{- \frac{0}{1}}

4 π \cdot 1 0^{- 7} \cdot (2.4 \cdot 1 0^{- 3})

4 π^{2} (1.8 s^{- 1})^{2} [1130 k g + 4 (72.4 k g)]

\frac{1}{( 2.5 \cdot 1 0 ^{- 5} ) ^{2}} \cdot (- 1) \cdot 1 0^{- 10}

(5 x - 3)^{2} (2 - x^{4})^{2}

What is 2*3*10^{-4}*e^{-1/10}*10^{-2} ?
The solution to 2*3*10^{-4}*e^{-1/10}*10^{-2} is 3/(500000e^{1/10)}