What is (20^7)/(7!)e^{-20} ?

The solution to (20^7)/(7!)e^{-20} is (16000000)/(63e^{20)}

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simplify (20^7)/(7!)e^{-20}

simplify

\frac{2 0 ^{7}}{7 !} e^{- 20}

\frac{16000000}{63 e ^{20}}

Decimal Notation

0.00052 \dots

Solution steps

\frac{2 0 ^{7}}{7 !} e^{- 20}

Apply exponent rule:

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

= \frac{1}{e ^{20}} \cdot \frac{2 0 ^{7}}{7 !}

Multiply fractions:

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

= \frac{2 0 ^{7} \cdot 1}{7 ! e ^{20}}

Multiply:

2 0^{7} \cdot 1 = 2 0^{7}

= \frac{2 0 ^{7}}{e ^{20} \cdot 7 !}

7! e^{20} = 5040 e^{20}

= \frac{2 0 ^{7}}{5040 e ^{20}}

Factor

2 0^{7} : 2^{14} \cdot 5^{7}

Factor

5040 : 2^{4} \cdot 3^{2} \cdot 5 \cdot 7

= \frac{2 ^{14} \cdot 5 ^{7}}{2 ^{4} \cdot 3 ^{2} \cdot 5 \cdot 7 e ^{20}}

Cancel

\frac{2 ^{14} \cdot 5 ^{7}}{2 ^{4} \cdot 3 ^{2} \cdot 5 \cdot 7 e ^{20}} : \frac{2 ^{10} \cdot 5 ^{6}}{3 ^{2} \cdot 7 e ^{20}}

= \frac{2 ^{10} \cdot 5 ^{6}}{3 ^{2} \cdot 7 e ^{20}}

2^{10} \cdot 5^{6} = 16000000

= \frac{16000000}{3 ^{2} \cdot 7 e ^{20}}

3^{2} \cdot 7 e^{20} = 63 e^{20}

= \frac{16000000}{63 e ^{20}}

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

e^{- 2.2}

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

\frac{2}{x} \cdot \frac{5}{y}

What is (20^7)/(7!)e^{-20} ?
The solution to (20^7)/(7!)e^{-20} is (16000000)/(63e^{20)}