What is expand e^{-bz}*e^{-(x-z)^2 1/(4a)} ?

The solution to expand e^{-bz}*e^{-(x-z)^2 1/(4a)} is 1/(e^{\frac{4baz+(x-z)^2){4a}}}

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expand e^{-bz}*e^{-(x-z)^2 1/(4a)}

expand

e^{- b z} \cdot e^{- (x - z)^{2} \frac{1}{4 a}}

\frac{1}{e ^{\frac{4 ba z + ( x - z ) ^{2}}{4 a}}}

Solution steps

e^{- b z} e^{- (x - z)^{2} \frac{1}{4 a}}

Apply exponent rule:

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

= e^{- \frac{1}{4 a} (x - z)^{2}} \frac{1}{e ^{b z}}

Apply exponent rule:

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

= \frac{1}{e ^{b z}} \cdot \frac{1}{e ^{\frac{1}{4 a} (x - z)^{2}}}

\frac{1}{e ^{(x - z)^{2} \frac{1}{4 a}}} = \frac{1}{e ^{\frac{( x - z ) ^{2}}{4 a}}}

= \frac{1}{e ^{b z}} \cdot \frac{1}{e ^{\frac{( x - z ) ^{2}}{4 a}}}

Multiply fractions:

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

= \frac{1 \cdot 1}{e ^{b z} e ^{\frac{( x - z ) ^{2}}{4 a}}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{e ^{\frac{( x - z ) ^{2}}{4 a}} e ^{b z}}

e^{b z} e^{\frac{( x - z ) ^{2}}{4 a}} = e^{b z + \frac{( x - z ) ^{2}}{4 a}}

= \frac{1}{e ^{b z + \frac{( x - z ) ^{2}}{4 a}}}

e^{b z + \frac{( x - z ) ^{2}}{4 a}} = e^{\frac{4 ba z + ( x - z ) ^{2}}{4 a}}

= \frac{1}{e ^{\frac{b z \cdot 4 a + ( x - z ) ^{2}}{4 a}}}

e^{- x} (c x e^{2 x} + 2 c e^{2 x} + d)

0.9 3^{- 2}

4 \cdot 3.14 \cdot 10 \cdot 1 0^{- 7} \cdot 3500 \cdot 0.75

(1.26 \cdot 1 0^{- 4}) \cdot (60.052)

What is expand e^{-bz}*e^{-(x-z)^2 1/(4a)} ?
The solution to expand e^{-bz}*e^{-(x-z)^2 1/(4a)} is 1/(e^{\frac{4baz+(x-z)^2){4a}}}