What is 4/3 pi(sqrt(s/(4pi)))^3 ?

The solution to 4/3 pi(sqrt(s/(4pi)))^3 is (s^{3/2})/(6pi^{1/2)}

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simplify 4/3 pi(sqrt(s/(4pi)))^3

simplify

\frac{4}{3} π (\frac{s}{4 π})^{3}

\frac{s ^{\frac{3}{2}}}{6 π ^{\frac{1}{2}}}

Solution steps

\frac{4}{3} π (\frac{s}{4 π})^{3}

(\frac{s}{4 π})^{3} : (\frac{s}{4 π})^{\frac{3}{2}}

= \frac{4}{3} π (\frac{s}{4 π})^{\frac{3}{2}}

(\frac{s}{4 π})^{\frac{3}{2}} = \frac{s ^{\frac{3}{2}}}{8 π ^{\frac{3}{2}}}

= π \frac{4}{3} \cdot \frac{s ^{\frac{3}{2}}}{8 π ^{\frac{3}{2}}}

Multiply fractions:

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

= \frac{4 s ^{\frac{3}{2}} π}{3 \cdot 8 π ^{\frac{3}{2}}}

Multiply the numbers:

3 \cdot 8 = 24

= \frac{4 π s ^{\frac{3}{2}}}{24 π ^{\frac{3}{2}}}

Cancel the common factor:

4

= \frac{π s ^{\frac{3}{2}}}{6 π ^{\frac{3}{2}}}

Apply exponent rule:

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

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

= \frac{s ^{\frac{3}{2}}}{6 π ^{\frac{3}{2} - 1}}

Subtract the numbers:

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

= \frac{s ^{\frac{3}{2}}}{6 π ^{\frac{1}{2}}}

\frac{R ^{2}}{R ^{2} + ( \frac{1}{W C} ) ^{2}}

2.4 \cdot 1 0^{- 10}

0.2 (t - 2) \cdot (0.2 (t^{2} - 4 t + 4))

\frac{13}{6}

\frac{- 22}{2}

What is 4/3 pi(sqrt(s/(4pi)))^3 ?
The solution to 4/3 pi(sqrt(s/(4pi)))^3 is (s^{3/2})/(6pi^{1/2)}