What is (4e^{pi/4})/(sqrt(2))*e^{-pi/4} ?

The solution to (4e^{pi/4})/(sqrt(2))*e^{-pi/4} is 2*2^{1/2}

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simplify (4e^{pi/4})/(sqrt(2))*e^{-pi/4}

simplify

\frac{4 e ^{\frac{π}{4}}}{2} \cdot e^{- \frac{π}{4}}

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

Solution steps

\frac{4 e ^{\frac{π}{4}}}{2} e^{- \frac{π}{4}}

Apply exponent rule:

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

= \frac{1}{e ^{\frac{π}{4}}} \cdot \frac{4 e ^{\frac{π}{4}}}{2}

Multiply fractions:

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

= \frac{4 e ^{\frac{π}{4}} \cdot 1}{2 e ^{\frac{π}{4}}}

Cancel the common factor:

e^{\frac{π}{4}}

= \frac{4 \cdot 1}{2}

Multiply the numbers:

4 \cdot 1 = 4

= \frac{4}{2}

Factor

4 : 2^{2}

= \frac{2 ^{2}}{2}

Cancel

\frac{2 ^{2}}{2} : 2^{\frac{3}{2}}

= 2^{\frac{3}{2}}

2^{\frac{3}{2}} = 2^{1 + \frac{1}{2}}

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

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

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

Refine

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

1500 e^{- 0.58 (8)}

(3 - cos (x)) \cdot 45 e^{- 3 x}

\frac{( e ^{x^{2}} )}{e ^{x}}

(1.36 \cdot 1 0^{45}) (1.6 \cdot 1 0^{- 40})

2.269 \cdot 1 0^{- 8} \cdot 0.53

What is (4e^{pi/4})/(sqrt(2))*e^{-pi/4} ?
The solution to (4e^{pi/4})/(sqrt(2))*e^{-pi/4} is 2*2^{1/2}