What is 6.4*1.6*10^{-19} ?

The solution to 6.4*1.6*10^{-19} is 1/(5^{19)*51200}

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simplify 6.41.610^{-19}

simplify

6.4 \cdot 1.6 \cdot 1 0^{- 19}

\frac{1}{5 ^{19} \cdot 51200}

Decimal Notation

1.024 E - 18

Solution steps

6.4 \cdot 1.6 \cdot 1 0^{- 19}

Multiply the numbers:

6.4 \cdot 1.6 = 10.24

= 10.24 \cdot 1 0^{- 19}

= 1 0^{- 19} \cdot 10.24

Apply exponent rule:

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

1 0^{- 19} = \frac{1}{1 0 ^{19}}

= \frac{1}{1 0 ^{19}} \cdot 10.24

\frac{1}{1 0 ^{19}} \cdot 10.24 = \frac{10.24}{1 0 ^{19}}

= \frac{10.24}{1 0 ^{19}}

\frac{10.24}{1 0 ^{19}} = \frac{1024}{100 \cdot 1 0 ^{19}}

= \frac{1024}{100 \cdot 1 0 ^{19}}

Factor the number:

1024 = 4 \cdot 256

= \frac{4 \cdot 256}{100 \cdot 1 0 ^{19}}

Factor the number:

100 = 4 \cdot 25

= \frac{4 \cdot 256}{4 \cdot 25 \cdot 1 0 ^{19}}

Cancel the common factor:

4

= \frac{256}{25 \cdot 1 0 ^{19}}

Factor the number:

256 = 2^{8}

= \frac{2 ^{8}}{25 \cdot 1 0 ^{19}}

Factor

1 0^{19} : 2^{19} \cdot 5^{19}

= \frac{2 ^{8}}{25 \cdot 2 ^{19} \cdot 5 ^{19}}

\frac{2 ^{8}}{2 ^{19}} = \frac{1}{2 ^{11}}

= \frac{1}{25 \cdot 2 ^{11} \cdot 5 ^{19}}

25 \cdot 2^{11} \cdot 5^{19} = 5^{19} \cdot 51200

= \frac{1}{5 ^{19} \cdot 51200}

27 e^{- 3}

2 ab (3 \frac{a}{b} - 2 \frac{b}{a ^{3}})

1 + x^{2} \cdot 1 - x

(2 x + 1) e^{- x}

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