What is 2e^{-1}*(3e^3)^2 ?

The solution to 2e^{-1}*(3e^3)^2 is 18e^5

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simplify 2e^{-1}*(3e^3)^2

simplify

2 e^{- 1} \cdot (3 e^{3})^{2}

18 e^{5}

Decimal Notation

2671.43686 \dots

Solution steps

2 e^{- 1} (3 e^{3})^{2}

Apply exponent rule:

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

= 2 \cdot \frac{1}{e} (3 e^{3})^{2}

(3 e^{3})^{2} = 3^{2} e^{6}

= 3^{2} \cdot 2 e^{6} \frac{1}{e}

Multiply fractions:

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

= \frac{1 \cdot 2 \cdot 3 ^{2} e ^{6}}{e}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{3 ^{2} \cdot 2 e ^{6}}{e}

Cancel the common factor:

e

= 3^{2} \cdot 2 e^{5}

3^{2} = 9

= 9 \cdot 2 e^{5}

Multiply the numbers:

9 \cdot 2 = 18

= 18 e^{5}

x (5 x^{3})

\frac{e ^{- 24}}{e ^{- 8}}

(e^{3})^{- 2}

e^{- j w} \cdot e^{j w}