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Popular >

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

Solution

simplify

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

Solution

\frac{4}{9 e ^{2}}

+1

Decimal Notation

0.06014 \dots

Solution steps

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

Apply exponent rule:

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

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

(\frac{2}{3})^{2} = \frac{2 ^{2}}{3 ^{2}}

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

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

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

Multiply fractions:

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

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

Multiply:

2^{2} \cdot 1 = 2^{2}

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

2^{2} = 4

= \frac{4}{3 ^{2} e ^{2}}

3^{2} = 9

= \frac{4}{9 e ^{2}}

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Frequently Asked Questions (FAQ)

What is (2/3)^2e^{-3(2/3)} ?
The solution to (2/3)^2e^{-3(2/3)} is 4/(9e^2)