What is 15^{10}*1/(10!)*e^{-15} ?

The solution to 15^{10}*1/(10!)*e^{-15} is (284765625)/(1792e^{15)}

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simplify 15^{10}1/(10!)e^{-15}

simplify

1 5^{10} \cdot \frac{1}{10 !} \cdot e^{- 15}

\frac{284765625}{1792 e ^{15}}

Decimal Notation

0.04861 \dots

Solution steps

1 5^{10} \cdot \frac{1}{10 !} e^{- 15}

Apply exponent rule:

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

= 1 5^{10} \cdot \frac{1}{10 !} \cdot \frac{1}{e ^{15}}

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 1 5 ^{10}}{10 ! e ^{15}}

Multiply:

1 \cdot 1 \cdot 1 5^{10} = 1 5^{10}

= \frac{1 5 ^{10}}{e ^{15} \cdot 10 !}

10! e^{15} = 3628800 e^{15}

= \frac{1 5 ^{10}}{3628800 e ^{15}}

Factor

1 5^{10} : 3^{10} \cdot 5^{10}

Factor

3628800 : 2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 7

= \frac{3 ^{10} \cdot 5 ^{10}}{2 ^{8} \cdot 3 ^{4} \cdot 5 ^{2} \cdot 7 e ^{15}}

Cancel

\frac{3 ^{10} \cdot 5 ^{10}}{2 ^{8} \cdot 3 ^{4} \cdot 5 ^{2} \cdot 7 e ^{15}} : \frac{5 ^{8} \cdot 3 ^{6}}{2 ^{8} \cdot 7 e ^{15}}

= \frac{5 ^{8} \cdot 3 ^{6}}{2 ^{8} \cdot 7 e ^{15}}

5^{8} \cdot 3^{6} = 284765625

= \frac{284765625}{2 ^{8} \cdot 7 e ^{15}}

2^{8} \cdot 7 e^{15} = 1792 e^{15}

= \frac{284765625}{1792 e ^{15}}

2000 e^{- 0.06 (3)}

π^{- \frac{1}{4}}

- 2.18 \cdot 1 0^{- 18} (\frac{1}{1 ^{2}} - \frac{1}{3 ^{2}})

3 \cdot x^{2} + 1

What is 15^{10}*1/(10!)*e^{-15} ?
The solution to 15^{10}*1/(10!)*e^{-15} is (284765625)/(1792e^{15)}