What is 2/(sqrt(3))(\sqrt[5]{3})^{3/2} ?

The solution to 2/(sqrt(3))(\sqrt[5]{3})^{3/2} is 2/(3^{1/5)}

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simplify 2/(sqrt(3))(\sqrt[5]{3})^{3/2}

simplify

\frac{2}{3 ^{\frac{1}{5}}}

Decimal Notation

1.60548 \dots

Solution steps

= \frac{2}{3} \cdot 3^{\frac{3}{10}}

Multiply fractions:

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

= \frac{2 \cdot 3 ^{\frac{3}{10}}}{3}

Apply exponent rule:

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

\frac{3 ^{\frac{3}{10}}}{3} = \frac{3 ^{\frac{3}{10}}}{3 ^{\frac{1}{2}}} = \frac{1}{3 ^{\frac{1}{2} - \frac{3}{10}}}

= \frac{2}{3 ^{\frac{1}{2} - \frac{3}{10}}}

Subtract the numbers:

\frac{1}{2} - \frac{3}{10} = \frac{1}{5}

= \frac{2}{3 ^{\frac{1}{5}}}

e^{0.46996} \cdot e^{36.14369}

e^{- \frac{17}{3}}

e^{- (60) \cdot 2}

(25 (2)^{t}) \cdot (150 (1.5)^{t})

What is 2/(sqrt(3))(\sqrt[5]{3})^{3/2} ?
The solution to 2/(sqrt(3))(\sqrt[5]{3})^{3/2} is 2/(3^{1/5)}