What is e^{-7.5}(7.5)^{(6!)/(6!)} ?

The solution to e^{-7.5}(7.5)^{(6!)/(6!)} is 0.00414…

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simplify e^{-7.5}(7.5)^{(6!)/(6!)}

simplify

e^{- 7.5} (7.5)^{\frac{6 !}{6 !}}

0.00414 \dots

Solution steps

e^{- 7.5} (7.5)^{\frac{6 !}{6 !}}

Apply exponent rule:

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

= 7. 5^{\frac{6 !}{6 !}} \cdot \frac{1}{e ^{7.5}}

Apply rule

\frac{a}{a} = 1

\frac{6 !}{6 !} = 1

= 7. 5^{1} \cdot \frac{1}{e ^{7.5}}

Apply rule

a^{1} = a

= 7.5 \cdot \frac{1}{e ^{7.5}}

Multiply fractions:

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

= \frac{1 \cdot 7.5}{e ^{7.5}}

Multiply the numbers:

1 \cdot 7.5 = 7.5

= \frac{7.5}{e ^{7.5}}

e^{7.5} = 1808.04241 \dots

= \frac{7.5}{1808.04241 \dots}

Divide the numbers:

\frac{7.5}{1808.04241 \dots} = 0.00414 \dots

= 0.00414 \dots

1.06 \cdot 1 0^{- 1}

e^{- \frac{x}{200}}

- y^{3} (x^{3} y^{2})

e^{- 0.409}

What is e^{-7.5}(7.5)^{(6!)/(6!)} ?
The solution to e^{-7.5}(7.5)^{(6!)/(6!)} is 0.00414…