What is sqrt(2pi)*10^{0.5}*e^{-(10^{0.5})^2} ?

The solution to sqrt(2pi)*10^{0.5}*e^{-(10^{0.5})^2} is (2*5^{1/2}pi^{1/2})/(e^{10)}

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simplify sqrt(2pi)10^{0.5}e^{-(10^{0.5})^2}

simplify

2 π \cdot 1 0^{0.5} \cdot e^{- (1 0^{0.5})^{2}}

\frac{2 \cdot 5 ^{\frac{1}{2}} π ^{\frac{1}{2}}}{e ^{10}}

Decimal Notation

0.00035 \dots

Solution steps

2 π \cdot 1 0^{0.5} e^{- (1 0^{0.5})^{2}}

Apply exponent rule:

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

= 1 0^{0.5} \cdot \frac{1}{e ^{(1 0^{0.5})^{2}}} 2 π

2 π = 2^{\frac{1}{2}} π^{\frac{1}{2}}

= 2^{\frac{1}{2}} \cdot 1 0^{\frac{1}{2}} π^{\frac{1}{2}} \frac{1}{e ^{(1 0^{\frac{1}{2}})^{2}}}

\frac{1}{e ^{(1 0^{\frac{1}{2}})^{2}}} = \frac{1}{e ^{10}}

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

Factor integer

10 = 2 \cdot 5

= 2^{\frac{1}{2}} π^{\frac{1}{2}} (2 \cdot 5)^{\frac{1}{2}} \frac{1}{e ^{10}}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(2 \cdot 5)^{\frac{1}{2}} = 2^{\frac{1}{2}} \cdot 5^{\frac{1}{2}}

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

Apply exponent rule:

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

2^{\frac{1}{2}} \cdot 2^{\frac{1}{2}} = 2^{\frac{1}{2} + \frac{1}{2}}

= π^{\frac{1}{2}} \cdot 2^{\frac{1}{2} + \frac{1}{2}} \cdot 5^{\frac{1}{2}} \cdot \frac{1}{e ^{10}}

2^{\frac{1}{2} + \frac{1}{2}} = 2

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 2 = 2

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

(p^{2} q) (pq)

e^{- (\frac{4}{10})^{2}}

7.68 \cdot 1 0^{- 6}

180 \cdot 1.0 2^{- 1}

\frac{( 0.8 ) ^{5}}{( 0.2 ) ^{5}}

What is sqrt(2pi)*10^{0.5}*e^{-(10^{0.5})^2} ?
The solution to sqrt(2pi)*10^{0.5}*e^{-(10^{0.5})^2} is (2*5^{1/2}pi^{1/2})/(e^{10)}