What is 10*1/4 e^{-4*1/4} ?

The solution to 10*1/4 e^{-4*1/4} is 5/(2e)

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simplify 101/4 e^{-41/4}

simplify

10 \cdot \frac{1}{4} e^{- 4 \cdot \frac{1}{4}}

\frac{5}{2 e}

Decimal Notation

0.91969 \dots

Solution steps

10 \cdot \frac{1}{4} e^{- 4 \cdot \frac{1}{4}}

Apply exponent rule:

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

= 10 \cdot \frac{1}{4} \cdot \frac{1}{e ^{4 \cdot \frac{1}{4}}}

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

= 10 \cdot \frac{1}{4} \cdot \frac{1}{e}

Multiply fractions:

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

= \frac{1 \cdot 1 \cdot 10}{4 e}

Multiply the numbers:

1 \cdot 1 \cdot 10 = 10

= \frac{10}{4 e}

Cancel the common factor:

2

= \frac{5}{2 e}

4 e^{- 4 t}

(2 e^{2 \cdot 20} - 1)^{- \frac{1}{2}}

e^{- s i n (x)} (e^{s i n (x)} + c)

66^{\frac{1}{2}}

e^{- \frac{13}{2}}