What is e^{-4}*(4^6)/(6!) ?

The solution to e^{-4}*(4^6)/(6!) is (256)/(45e^4)

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simplify e^{-4}*(4^6)/(6!)

simplify

e^{- 4} \cdot \frac{4 ^{6}}{6 !}

\frac{256}{45 e ^{4}}

Solution steps

e^{- 4} \frac{4 ^{6}}{6 !}

Apply exponent rule:

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

= \frac{1}{e ^{4}} \cdot \frac{4 ^{6}}{6 !}

Multiply fractions:

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

= \frac{1 \cdot 4 ^{6}}{e ^{4} \cdot 6 !}

Multiply:

1 \cdot 4^{6} = 4^{6}

= \frac{4 ^{6}}{e ^{4} \cdot 6 !}

4^{6} = 4096

= \frac{4096}{e ^{4} \cdot 6 !}

e^{4} \cdot 6! = 720 e^{4}

= \frac{4096}{720 e ^{4}}

Cancel the common factor:

16

= \frac{256}{45 e ^{4}}

(3 x^{2}) (2 x^{5})

(y^{3}) (- 3 y^{5}) (- 2 y^{4}) (y^{2})

2 e^{x} \times e^{x}

(9 \cdot 1 0^{5}) \cdot (9 \cdot 1 0^{7})

[(4^{2})^{2}]^{2}