What is 1.6e^{-19}*110e^3 ?

The solution to 1.6e^{-19}*110e^3 is 0.00001…

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simplify 1.6e^{-19}*110e^3

simplify

1.6 e^{- 19} \cdot 110 e^{3}

0.00001 \dots

Solution steps

1.6 e^{- 19} \cdot 110 e^{3}

Apply exponent rule:

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

e^{- 19} e^{3} = e^{- 19 + 3}

= 1.6 \cdot 110 e^{- 19 + 3}

Add/Subtract the numbers:

- 19 + 3 = - 16

= 1.6 \cdot 110 e^{- 16}

Apply exponent rule:

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

e^{- 16} = \frac{1}{e ^{16}}

= 110 \cdot 1.6 \cdot \frac{1}{e ^{16}}

Multiply fractions:

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

= 1.6 \cdot \frac{1 \cdot 110}{e ^{16}}

Multiply the numbers:

1 \cdot 110 = 110

= 1.6 \cdot \frac{110}{e ^{16}}

Multiply fractions:

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

= \frac{110 \cdot 1.6}{e ^{16}}

Multiply the numbers:

110 \cdot 1.6 = 176

= \frac{176}{e ^{16}}

Convert element to a decimal form

e^{16} = 8886110.52050 \dots

= \frac{176}{8886110.52050 \dots}

Divide the numbers:

\frac{176}{8886110.52050 \dots} = 0.00001 \dots

= 0.00001 \dots

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