What is 3(3)^3e^{-(3)} ?

The solution to 3(3)^3e^{-(3)} is (81)/(e^3)

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simplify 3(3)^3e^{-(3)}

simplify

3 (3)^{3} e^{- (3)}

\frac{81}{e ^{3}}

Decimal Notation

4.03275 \dots

Solution steps

3 (3)^{3} e^{- (3)}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3 \cdot 3^{3} = 3^{1 + 3}

= 3^{1 + 3} e^{- 3}

Add the numbers:

1 + 3 = 4

= 3^{4} e^{- 3}

Apply exponent rule:

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

e^{- 3} = \frac{1}{e ^{3}}

= 3^{4} \cdot \frac{1}{e ^{3}}

Multiply fractions:

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

= \frac{1 \cdot 3 ^{4}}{e ^{3}}

Multiply:

1 \cdot 3^{4} = 3^{4}

= \frac{3 ^{4}}{e ^{3}}

3^{4} = 81

= \frac{81}{e ^{3}}

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