What is e^{-2*(sqrt(ln(0.95)))^2} ?

The solution to e^{-2*(sqrt(ln(0.95)))^2} is 1.10803…

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simplify e^{-2*(sqrt(ln(0.95)))^2}

simplify

e^{- 2 \cdot (l n (0.95))^{2}}

1.10803 \dots

Solution steps

e^{- 2 (l n (0.95))^{2}}

Apply exponent rule:

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

= \frac{1}{e ^{2 (l n (0.95))^{2}}}

e^{2 (l n (0.95))^{2}} = 0.9 5^{- 2 i^{2}}

= \frac{1}{0.9 5 ^{- 2 i^{2}}}

Apply exponent rule:

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

0.9 5^{- 2 i^{2}} = \frac{1}{0.9 5 ^{2 i^{2}}}

= \frac{1}{\frac{1}{0.9 5 ^{2 i^{2}}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{0.9 5 ^{2 i^{2}}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 0.9 5^{2 i^{2}}

i^{2} = - 1

= 0.9 5^{2 (- 1)}

Simplify

= 1.10803 \dots

8.75 \cdot 1 0^{- 6}

8.75 \cdot 1 0^{- 3}

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

\frac{x + 1}{7 - x}

462.43 \cdot 1 0^{- 3}

What is e^{-2*(sqrt(ln(0.95)))^2} ?
The solution to e^{-2*(sqrt(ln(0.95)))^2} is 1.10803…